I think I'd try the carrot and stick approach. Since she deceived you and lied to facebook, it would take some time to build your trust and earn the privilege.
Set up some preconditions and a time limits and then allow her to earn some sort of account. There would be many parental conditions, checks and controls.
That said, I'm pretty set in my doling out privileges, especially those that involve safety. Personally, I think she is too young and immature for a fb account and would simply say no; you'll have to wait until you're x years old.