Who are her atheist heroes? Dawkins or Hitchens? Epicurus or Democritus? Freud or Marx? Stephen J. Gould or E. O. Wilson?
Exactly. There is many types of atheists and reasons to be atheist.
When I was an atheist, I would have laughed if someone handed me C.S. Lewis or Ravi Zachariah. Maybe it might work on someone else, but Christian apologetics are not as effective as they might seem to those already convinced- they can instead provide an occasion for atheists to strengthen their arguments and their atheism.
Let me make something clear: For someone who is not particularly searching for faith, unsolicited apologetic literature is a killer.
It's a drag. It's like getting homework from your friends. It's patronizing. There needs to be dialogue in a friendship or relationship, and "Read this book and tell me what you think" doesn't really cut it. So make sure she is actually curious before even thinking of giving her a book recommendation.
What brought me to religion in general and eventually Christianity were glimpses into a lived faith- the peace, beauty, and community arising from a revelation, expressed in worship, art, and kind acts. Literature can be part of this too but it has to be the right books for the right person. William Blake and John Milton were big influences for me but not necessarily for someone else.
I've often thought about what book I might recommend to an atheist/ agnostic who was philosophically or aesthetically inclined. I would probably go with Fr. Sophrony's His Life is Mine.
But this is all assuming that said atheist is asking for a book.