Why Did Voldemort Give Lily A Chance To Live?

I've been trying to find an answer for this at the books, and I don't see it clear...
He really needn't to do it, he could have just killed her, so why did he give a chance?
That's not "normal" in Voldemort (I mean, if we consider "normal" killing people, horcruxes... what he does is never normal).
But he told her something like this "Give me the baby and you could live". Why should she remain alive? Why was she special/different?
I read before, somewhere here, some theories about Snape being in love with her, and I agree with that, but could he maybe told Voldemort not to kill her?

Do you know anything more about this?

after reading, re-reading, doing homework, re-re-re-reading the books, eating, doing other stuff, and carefully pondering your theory, i believe i've come up with a very simple answer...i don't know...haha...but no really...it's possible you could be right. personally, i think it was VOLDEMORT, not snape, but VOLDEMORT who was in love with lily. just a thought. plz reply...

Well, here goes you answer...
My theory about Lily-Snape comes from book 5th or 6th, I don't remmember well, but I have never read that Voldemort has ever met Lily or James before killing them.
Anyway, thank you for your opinion.

ginevra: We do know that Lily and James had had some kind of dealings with Voldemort because according to the prophecy they had "thrice defied him". We don't know anything about what Lily and James did after leaving school (Harry's never asked which is weird) so this reference to them is tantilising.
'Defy' is a strange term to use don't you think?