I’d argue it’s the opposite- Lily is the only reason Snape has any shred of good in him.
We see that Snape grew up in a difficult environment. In one of the Occlumency classes with Snape in The Order of the Phoenix, Harry breaks back into Snape’s memories and witnesses a scene of Snape as a small boy, cowering as his father shouts at his mother. That scene fits in with a conversation between a young Lily and Snape in the Prince’s Tale chapter of The Deathly Hallows (as noted in another answer):
“They’re not arguing anymore?”
“Oh, yes they’re arguing,” said Snape. He picked up a fistful of leaves and began tearing them apart, apparently unaware of what he was doing. "But it won’t be that long and I’ll be gone."
"Doesn’t your dad like magic?"
"He doesn’t like anything, much," said Snape.
On top of his home life, Snape integrated himself into a group of nasty Slytherians at school. In the chapter "Padfoot Returns" in The Goblet of Fire, Sirius mentions that “Snape’s always been interested in the Dark Arts, he was famous for it at school.” This fits with the series of Lily/Snape memories from "The Prince’s Tale," starting with an argument that precedes the "Mudblood" incident:
“… thought we were supposed to be friends?” Snape was saying. “Best friends?”
“We are, Sev, but I don’t like some of the people you’re hanging round with! I’m sorry, but I detest Every and Mulciber! Mulciber! What do you see in him, Sev, he’s creepy! D’you know what he tried to do to Marry Macdonald the other day?”
Lily had reached a pillar and leaned against it, looking up into the thin, sallow face.
“That was nothing,” said Snape. “It was a laugh, that’s all—”
“It was Dark Magic, and if you think that’s funny—”
“I know James Potter’s an arrogant toerag,” she said, cutting across Snape. “I don’t need you to tell me that. But Mulciber’s and Avery’s idea of humor is just evil. Evil, Sev. I don’t understand how you can be friends with them.”
This scene is a setup to this conversation, which follows the "Mudblood" incident and is the end of Snape’s direct interaction with Lily, as far as we see in the books.
“You don’t even deny that’s what you’re all aiming to be! You can’t wait to join You-Know-Who, can you?”
This response is getting long, but Snape is a character who had a difficult childhood, then found schoolmates who were similarly disposed toward evil acts. He goes on to become a Death Eater, and there’s nothing in the books to indicate he has any second thoughts about this decision up until he relays the prophecy to Voldemort. At this point, his love for Lily, which is the only good thing in him, is enough for him to set aside his life as a Death Eater to become a double agent.
As Dumbledore says in the memory that reveals Snape’s true allegiance in "The Prince’s Tale":
“My word, Severus, that I shall never reveal the best of you?" Dumbledore sighed, looking down into Snape’s ferocious, anguished face. "If you insist …”