Oh god I didn't think people would actually want to hear it. It's actually so fucking much to go into lol. Buckle up if you're going to dive in. The theory, potential book/universe spoilers:
So the theory doesn't really have any singular floor, just a lot of bridges that can almost form one. And that alone is a support to the theory, because if it was true, it's something GRRM wouldn't write in directly as it's something the in-world characters couldn't see or comprehend.
To start off, there's several locations in A World of Ice and Fire that are directly inspired by Lovecraftian lore. These include Carcosa, K'Dath, and Leng, all direct names from Lovecraft's work. Additionally, a super key location is Stygai, a corpse city further in the Shadowlands of Asshai (which is also connected to this theory), which is extremely likely to be a reference to Stygia, a city from Robert E. Howard's Conan the Barbarian, which is heavily related to shadows. Robert E. Howard was also a friend of H.P. Lovecraft, which is a minor connection, but fairly significant.
The second most obvious connection, which people have connected to Lovecraft since Book 1, is the Ironborn and the Drowned God. The Drowned God is almost explicitly referencing the most iconic character of the Lovecraftian universe: Cthulhu. However, there's a key bit of information about the Ironborn that is far more important to this theory. The Seastone Chair is the throne from which the Iron Islands was ruled, and the Iron Fleet obey whoever sits upon it (whoever is King, really). It's clearly a very symbolic thing, but it's what it's made out of that's important. The Seastone Chair is made of a mysterious, oily black stone, that happens to show up a lot in ASoIaF. In fact, it shows up all over the world.
In Northern Sothoryos, further inland than the abandoned city of Zamettar, is the abandoned city of Yeen. Nymeria took her Rhoynish refugees across the Summer Sea, looking to colonize any land that would allow them, but only disaster met them at Sothoryos. While Zamettar was the main city in Sothoryos that the Rhoynar attempted to rebuild, Nymeria sent several men to Yeen looking to colonize it. However, not much long later, it was apparent that Sothoryos's jungle climate, filled with dangerous predators, parasites, and pathogens, weren't worth sticking around for. The Zamettar settlers sailed up the delta towards Yeen to deliver the news that they were leaving, but when they arrived, Yeen was abandoned. There were no signs of struggle or conflict, things were abandoned where they were, but all life was gone. The jungle was growing inwards on the city, but refused to touch its foundation or buildings, which were made of oily, black stone.
Just north of Sothoyros, in the Basilisk Isles, is the Isle of Toads. The Isle, inhabited by people with webbed appendages who resemble fish, is home to a massive idol of a Toad, made of the same oily, black stone. In the northeast-most explored lands of the known world, are the Thousand Islands, a massive archipelago, where many things seem alien to what we see in Westeros. While not exactly fish like, the inhabitants of these islands are hairless, green-skinned xenophobes, who file their teeth into sharp points and have allegedly sacrificed sailors to their fish-headed gods. Under the water, the likenesses of these gods can be made out, carved into the rocks beneath the waves. However, interestingly, these people have an extreme phobia of water, and even with the threat of being killed, will never step into the water. From the wiki, "Some believe they are the remnants of a drowned kingdom whose buildings were submerged by the rising sea thousands of years ago."
South of these islands are the lands of the Jogos N'hai and, further south, Yi Ti. It is said that the Great Empire of the Dawn made up these two lands, and more, and was led by the God-on-Earth, the only son of the Maiden-Made-of-Light, a deity celebrated for life and happiness, and the Lion of Night, a god feared for death and destruction. The lineage of this empire is recorded to be small and direct, with one emperor to succeed after the last, each empire ruling for fewer years than the previous. It's said that the God-on-Earth ruled for 10,000 years. However, this empire ended with the Bloodstone Emperor, who killed his sister and usurped the throne. This emperor worshiped a black stone that had fallen from the sky, and was said to have started the Long Night. Things falling from the sky and being worshiped are heavily based on Lovecraftian lore, and this is a fairly significant association between the Long Night and the Black Stone, which I'll get back to later.
The black stone continues to pop up in a few more significant places. In Yi Ti, on the northeastern border, sits five massive towers of black stone, each seemingly impossible to man, as a single tower could hold about ten thousand men. Though not necessarily connected to this theory per se, in Westeros, a massive, ruined curtain wall made of black basalt is located in the Neck, the marshy border between The North and the rest of Westeros.
Finally, a very key part in this theory, is the Battle Isle. In Oldtown, beneath the Hightower (the massive tower you can see in Episode 1 of Season 7), is the Battle Isle, a massive structure of slick, black stone. I can not explain it better than I could paraphrase it from the wiki: "[It is] a square, labrynthine fortress of fused black stone. Its appearance is reminiscent of the dragonroads of the Valyrian Freehold and the Black Walls of Volantis [...] but there is no archaeological evidence of Valyrians at Oldtown. [...] The fortress is plain and unadorned, unlike the fused stone constructions of the Valyrians, who twisted and shaped the fused stone to ornament their buildings.
Archmaester Quillion suggests a connection between the fortress and the mazemakers of Lorath. The legends of Lorath claim the mazemakers were destroyed by something from the sea. Maester Theron, a bastard of Ironborn ancestry, suggests in his Strange Stone that there is a connection between the Hightower's base and the Seastone Chair, and that they were created by the Deep Ones, a legendary race created by the breeding of sea creatures with humans and which may have inspired the legends of merlings."
This is particularly crucial evidence, as it kind of blows the doors on the theory wide open. Deep Ones are a very direct reference to Lovecraft's mythology. Let's take a quick look at a chapter from A Feast for Crows, in which Brienne of Tarth is visiting Crackclaw Point. Dick Crabb, a former soldier (and potential descendant of House Crabb, previous owners of The Whispers, which is a sinister castle with a sinister history located on Crackclaw Point), warns the two about Squishers. From the wiki, again paraphrased: "From a distance squishers appear human, but according to legend their heads are larger than those of men and they have scales instead of hair. They have webbing between their fingers and toes, while their mouths have rows of green, needle-like teeth. A squisher's belly is white like that of a fish. Their name comes from the squish-squish sound made when they move on their webbed feet.
The First Men are said to have killed all of the squishers, but some residents of Crackclaw claim still squishers come by night to steal bad children, saving girls to breed with and boys to eat.
Some or all members of House Borrell (of Sweetsister, one of three "sister" islands located between the Vale and the North) have webbed hands and toes similar to the feet of ducks, which they call the 'mark.' It is unknown if this is a genetic disorder or if they have a connection with squishers.
It is likely the stories of Squishers are related to the Deep Ones."
Now things are falling a bit into place, right? Across the world, scattered about, are races that resemble both fish and man, and an oily black stone, too, is all over, sticking to primarily coastal regions. So, what does this mean? Well, it can be inferred that when looking at the regions the black stone and squishers or fish-like peoples appear, all of it seems to show up around water, or at least, not far from it. Crucially, it appears in places like Yeen, and Asshai, and Battle Isle. But these places are extremely far apart, so how exactly are they to be connected? No known empire has possessed lands from different continents, not even the Valyrian Freehold, as far as we know (excluding Dragonstone, which was barely in Westeros). So, are they different societies who happened to build with the same materials, or, were they built by a society or societies that live primarily underwater? Let's take a quick look at one of those places: Asshai.
Allegedly, Asshai's great walls could allegedly fit Volantis, Qarth, King's Landing, and Oldtown combined. That's several, several million people. By the time of AGoT, the city is barely populated compared to the size of it, and is only really home to people looking to make use of its magical capabilities. That's right, the city is particularly magical. In ASoIaF, there is apparently PLENTY of magic that has simply left the world since the fall of the Valyrian Freehold. Melissandre talks about this while at Castle Black; she can feel more magical potency from Beyond the Wall, just like she can feel more of it in other specific places of the world, too. But what could be the source of this magical strength in either of these places? Well, Beyond the Wall is going to have to be explained in a second, but I have a hypothesis of my own about Asshai. Stygai, I believe, is the R'lyeh of Planetos. In Lovecraft's Mythos, R'lyeh is the subterranean prison of Cthulhu located in the South Pacific. And this brings us to the first side of the battle: the Drowned God. Whether this unnamed, unseen, unconfirmed deity is particularly Cthulhu-like, the connection between Asshai and the "squishers" is amplified when taking Stygai into account. Stygai is a place not even the bravest of Asshai mages go--and Asshai is a place few people can survive to begin with, with its poisonous water, lack of healthy food supply, and constant shadow. Asshai, or Stygai, exudes corruption, but also magic. Often sinister magic, but magic nonetheless. And I believe that Stygai is the home of the Drowned God, who had sent his squishers across Planetos to build and conquer.
So, what happened to them? Well, like the Roman Empire, like Napoleonic France, like the Third Reich, like the USSR, things are bound to fail with enough resistance against them. Simply put, something came to put them in their place. And my bet on that, is man. Ghiscar, Rhoyne, the First Men of Westeros, the Yi Ti (as we now know them), the Andals (pre-invasion), the Hyrkooni, the Qartheen, some of these people began to appear at some point between the Dawn and the Long Night, and pretty quickly began to expand across land and sea. It was these men who likely fought off the Drowned God's people, but they had an open weakness to exploit. They were greatly disorganized, with petty kings in charge at best in places like Westeros and Northern Essos, and the Drowned God, as we'll continue to call him, wanted to exploit that, to beat his opponent. This option would become available when a few Children of the Forest would stumble across him.
In a recent Bran chapter (don't want to bother digging it up), Bran has a vision of him flying above the world. He sees many things, and travels in a relatively linear line. Going from west to east, he eventually reaches Asshai, but keeps going, and finds himself back at the wall. So yes, he's Christopher Columbus. Not only is this important in terms of Planetos being round, but it could mean that if you were to travel north, east, or northeast from Asshai, you'll eventually reach the wall. So, in a theory that can be related to this one, the Children of the Forest that would continue north in hopes of escaping the First Men when things looked their most dire could have stumbled upon Asshai, or more specifically, Stygai. Ever wonder why the White Walkers are called the "Others" in the books? Well, one possibility, is that they're the "other" Children of the Forest, who were transformed into very powerful ice-like, demon-like beings, capable of raising the dead of those who they kill to fight for them. Remember what I said about North of the Wall being particularly magical? Well, that's because it's closer to Asshai than we would think.
I know this is a lot already, like, way more than most people are going to want to read, but in sake of ease over speed to read, I'll roughly explain the area around this mysterious land between Asshai and the North. Blocked to the west by the Five Forts is the Grey Wastes, the Cannibal Sands, Land of the Shrykes, City of the Winged Men, Cities of the Bloodless Men, the City of Bonetown, and the Cities of K'Dath and Carcosa, both direct Lovecraftian references, as mentioned way, way back in this post.
One of these locations is particularly important, and now that some other things have been explained, it should be easier to put this into context. Carcosa is currently home to The Yellow Emperor--a claimant to the Yi Ti empire, who is a reference to Robert W. Chambers' The King in Yellow, which is very Lovecraftian in nature. Though not truly important to much, it's interesting to know that this exiled claimant fled to Carcosa, and that he is magically adept. Is he simply trying to make use of the magical power between Asshai and the North (if the theory holds up), or is he trying to make a deal with the unknown, as the Bloodstone Emperor may have?
Getting back on topic, the Drowned God made a pact with these "other" CotF. They would gain extreme powers that would threaten the world and surely allow them to dominate it, running out mankind, and the Drowned God would be winning. But what does the Drowned God get? He would be beating the Lord of Light, R'hllor. Hell, so that's why R'hllor sounds so damn Lovecraftian!
Note, that it's believed the Bloodstone Emperor was the one who ushered in the Long Night, so it's likely his rule and the pact between the Others and the Drowned God happened around the same time--that's not that important, but just so things are in perspective. R'hllor, possibly the Hastur the Unspeakable of this universe (though I don't fully understand the Hastur/Cthulhu dynamic other than they're brothers and don't get along), then fought back with Azor Ahai. Why, though, Azor Ahai is regarded as an Asshai'i, is unsure--but it should be noted that many cultures had their own Azor Ahai name, like Hyrkoon the Hero, Yin Tar, Neferion, and Eldric Shadowchaser. Melisandre, however, is another character in service to the Lord of Light who hails from Asshai. It's certainly possible that it's R'hllor in Stygai instead, and the Drowned God is underwater, but that doesn't line up so well with the rest of the theory. It's equally possible that the Asshai of later days were decent, light-loving people. On the flipside, the Ironborn worship the Drowned God, who would be the enemy they're meant to fight, if they are servants to R'hllor.
R'hllor wouldn't be able to hold this victory for long, however. His "servants," though seemingly indirect ones (though Lovecraftian Old Ones are known to be passive, subtle controllers and guiders), erected the Wall, similar to the Five Forts in Yi Ti, who may have served a similar function at some point far before. I would say it wasn't until the rise of the Valyrian Freehold that R'hllor pulled out ahead in the fight for the world. Think about it: no recorded "evils" between the Long Night ending and the collapse of the Valyrian Freehold, and more specifically, the death of the Targaryen dragons in Westeros, and even more specifically, the end of the Targaryen lineage.
It's probably important to know that in a recent interview about Beric Dondarrion in the future of the books, GRRM essentially said Beric is the light-version of the wights, the zombies the Others control. Like Jon, he has been revived, many times in fact, believed to be for a specific purpose. It's clear, however, that this version of a wight is far more conscious than its colder counterpart, as it retains more thought and personality, with only a "little piece" being taken away each time. There's many possibilities as to why the Other's wights are so much more unhuman, both in strengths and in personality, but my guess is that it's two takes on control. The Drowned God prefers outright domination of an individual and thus strips them of all individuality, personality, and weakness. R'hllor, however, prefers a subtler approach, wanting skill, tactic, and calculation in its subjects rather than a zerg horde. Alternatively, R'hllor could just be weaker at the moment, and reviving specific people is the best it can muster--which makes sense, if darkness is currently prevailing over light. "Why didn't R'hllor choose to resurrect Stannis, then?" - Well, that should be obvious, shouldn't it? Stannis wasn't really getting anywhere, he actually had to rely on other people on a lot of things. However, Stannis did something extremely important for R'hllor: he got Melissandre, a powerful sorceress with an affinity for the light, to meet Jon Snow, and in the show, and most likely the books, she will be needed to resurrect him. I'm sure I don't have to explain the "Jon Snow is the Prince Who Was Promised, otherwise known as Azor Ahai come again" theory to those who actually read all this.
I think I've got most of the theory out, and this is probably the farthest and most in-depth I've explained it. I've heard that a lot of people have had similar theories about this, but I haven't heard anything to the scale or measure as this, and there's a lot of things missing from those versions of the theory than what I put here. I wanted to put this into the form of a video a while back, so it'd be easier to explain this theory/put it out there for more people to hear, but it's so much stuff to make sure I include, lol. Hopefully if I do ever do it, I can refer back to this post. Thanks if you read this far, sorry if I made any weird spelling/grammar/formatting mistakes, I rushed this. :-)