Lakland Strings are made by GHS which suggests that GHS make their own strings. D'Addario make strings for Fender. So the conclusion seems to be that there are string making companies and then other companies who, because strings aren't their first thing, have strings made for them.
So you can expect that the likes of GHS, D'Addario, La Bella, Thomastik, etc., make their own strings while the likes of Fender, Ernie Ball, Lakland don't make their own strings.