N.M.
My best guess is that she doesn't like the fact that your house has rules (like no sneaking boyfriends in or lying) and she's rebelling. Even if she doesn't have a good relationship with her dad, she might think that he won't be as involved in her life, and that's what she thinks she wants.
How is your relationship with her dad? Could you talk to him about what is going on with her, tell him that you think she wants out of your house because she thinks she will have more freedom at his, and ask him to back you up in having her stay at your house? At the same time, she may really be looking for some male attention and validation right now, and it would be a lot better for everyone if she could get that from her dad, rather than from the boys she's trying to sneak into your house. So if Dad could be convinced to have a date with his daughter every few weeks, that might improve their relationship and the way she feels about herself. It also might improve the situation at your house because she'll see that Dad wants the best for her and he's not going to ignore everything she's doing wrong. If she sees that you and Dad are om the same page, she might just stop wishing to move out because she'll think that she'll have the same sort of rules at both houses.
Best of luck!
N.