I completed the game, and I could play LSPD FR fine, I lost my save and now back at the second mission and for some reason I die when I get to the top half of the map for the first time, and then its fine (until next time I play, then I die for the first time again). Not sure if that is due to not completing much of the story or not, but it started as soon as I lost my saved game.
But I think you should complete it first, it is a very good game.