Yes, Snape's motivation to save Harry was Lily. DH told us that. JKR stated yesterday that if Snape had not loved Lily he would not have acted to save Harry. I don't find this upsetting. It's like asking if Hermione's initials weren't HG, would she have monogrammed her towels with the initials HG. No, likely she wouldn't have.
Motivation starts somewhere. That does not mean that motivation remains the only factor, especially as years and years of one's life go by. See, everybody's talking about the scene when Snape produces a doe Patronus in response to Dumbledore's question if he's starting to care about Harry. To me it's evident that Snape did that in order to shut Dumbledore up because Snape doesn't want to talk about it, doesn't want to think about it, wants the fucking subject changed. And when he produces that Patronus, Dumbledore concedes; Dumbledore is admittedly tearful at Snape's steadfastness to Lily but also at Snape's refusal to see himself as a man who can change, who can let go of his hatred, who can do good for good's sake. And Dumbledore is thinking, "Yes, that's your Patronus. Impressive. But not an answer to the question, Severus. Still, I'll let it go. If I press you on this you'll only grow angrier."
Snape's distraction with the Patronus at that moment to me is perfect evidence that he has indeed shifted in his motivations--that they are indeed more complex than his devotion to Lily, even if they began that way--and that Snape, our wonderful prickly sour Snape, can't come near to acknowledging it.