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Then Snape tries to have them killed so that he could have Lily

I didn't read it that way. I read it as when he realized that the prophecy could pertain to Lily's child, and he realized Voldemort was going after him, Snape begged him to spare Lily. It wasn't that he WANTED James and the baby killed, but he knew that Voldemort was going to do it anyway, and he begged for the one person he seemed to have ever loved. When Voldemort killed Lily anyway, Snape went to Dumbledore in grief and remorse, and Dumbledore had him make restitution by placing himself in danger by re-joining the Death Eaters so as to keep tabs on Voldemort.

I don't have the book here but I recall the scene where Dumbledore says "You disgust me." IIRC, Dumbledore says something like, "it didn't matter to you that two people were going to die as long as the girl you loved lived." Snape then hesitates and says, "Okay, save them all."

He didn't care that Harry and James were going to be killed - his only worry was for Lily.