Has Lily anything to believe, that her death will save Harry?

In this answer DVK says, that "Lily's protection magic was triggered by her choosing to die to protect Harry". Has she got or knew anything, that would let her believe, that her sacrifice will save Harry? Or was it -- like JKR says in an interview mentioned by Slytherincess -- something, that any normal mother would have done for her child (no magic or mystery involved)?