Well, people are going to try and call her
Lily, regardless. You're going to be doing a lot of correcting people when you first meet them, but if that doesn't bother you than okay. I actually think she'd be far more likely to be called
Lily than Lil. Anyway:
Liliana- I can't stand
Liliana. I think it's the ultimate spoiled princess brat name. It's just so unnecessarily elaborate.
Lillian- Stately. It's grown on me lately. It's fairly no-nonsense. So obviously, I would choose
Lillian.