I have LFS on my F: drive and run game as admin. However the unlock is not saved the next time I run the game. Can't find anything similar searching the forum, any suggestions?

Could have something to do that LFS is not installed on "normal" drives like C or D? Not sure,but maybe that's the reason why regstry data is not stored.

dunno about windows 10 specifically, but in 7 it isn't an issue, i run LFS off E/F without a problem

Check if LFS folder is "read-only"