Love the name Lola, if you are a little worried about the song and what ppl may portray her to be like maybe choose something very similar like the others have suggested. Also love Laila and Lila, a friend of mine has a Laila and what a gorgeous little girl she has and i love Lila unfortunately DF didn't!
Come on who really cares if it is a nickname or not, look at the weird combinations ppl put together these days anyway and i seriously wouldn't have even thought of it as a nickname anyhow. Also a little girl isn't going to be portrayed as a sexy/stripper type figure at a delicate tender age!