JKR seems to be saying that there's more to it.
The explanation that Lily's sacrifice gave Harry protection seemed complete and straight-forward to me.
On my own, I would not have thought too hard about why Voldemort would tell her more than once to get out of the way. I thought it seemed like a silly question at first, but they keep asking and JKR gives her cryptic little answers.

So, from what I gather, Lily's death somehow lead to Snape's redemption. Like maybe Voldemort promised to leave Lily out of it as part of his deal with Snape. That's what some people seem to be implying.