'lijn' can mean any sort of line, while 'Linie' is specifically military. Ligne is French, and a lot of French words were used in those days, not always officially.
The 7th, being Belgian/South-NL, probably referred to itself als the 7e Batallion de Ligne. You know, because none of the officers had bothered to learn Dutch or anything.
The chief of staff of the Division uses the words 'linie' and 'ligne' indiscriminately in his diary. He also calls them
"7de Bataljon Zuid-Nederlandse Infantrie" a few times. One time he calls them regiment. This guy is just too unclear.