What exactly caused this falling out between the two of them? That might help us understand the situation better. Do they still live together?

Though it may not matter too much, it's pretty clear that you want L gone for numerous reasons. If you're not friends with this person, and you don't have to interact with them in any other way, I wouldn't stress it too much. I mean, don't be a jerk about it, but don't lose sleep over not inviting someone that NO ONE (save maybe one person) in your group wants to be around.