It goes further with her personality.
Lily is described as a sweet, innocent and mysterious character by almost anyone. Whilst others would say she is bipolar. Throughout most of the day she is a kind girl who gets along with almost everyone, and is even someone who people respect. But she isn't afraid to voice her opinion even if it makes the other person feel bad.
But the moment monster hunting is involved she isn't afraid to turn violent and insane, she is known for torturing monsters, even humans to get any information she needs.
Sweet/innocent and mysterious don't really go together. To be mysterious is to be aloof, and to be innocent is to be rather wide-open. Also, sweet and innocent people are afraid to "voice [their] opinion even if it makes the other person feel bad", it's part of being sweet and innocent. So she's innocent, yet mysterious, yet bold. Oh, and at the end it states that she can become a cold blooded killer if she needs to be. Key wording, there, seeing as it says "she isn't afraid to turn violent or insane" (Let alone, how does one suddenly turn insane? It's not an on/off switch). She tortures monsters and humans yet it doesn't list that she suffers any sort of psychological problems with this at all. Quite the opposite, she has no problems with ANYTHING at all. Further more and perhaps the biggest sign, she gets along with everyone and is respected by everyone. This is the definition of a Mary Sue.
Sorry if I come off as rude or an ass, but that's my standing on it.