Silent Observer said
Just started reading your post, wanted to let you know the Lillith doesn't play for either team in particular. She's a free spirit and she was purposefully flirting with your character. Gotta keep your enemies close. She's also a dealer on campus, just not the harder stuff like Cooper.
Don't go on telling what's true or not :P Facts, such as the house Lily is leaving in are good but players should be able to stab on the backgrounds of the other players hence the CS has no background but statements :P Such as the NPC's doubting Lisa's relationship with Maria.
Just a reminder, you can reenforce your background in-character though. If it passed the criteria, it may be canonized.