Severus realized being a death eater wasn't for him the day he told Voldemort part of the prophecy.
He knew Voldemort wouldn't spare Lily and Albus wasn't being a help. He didn't trust a word that man said, he let someone who tried to kill them stay in school with him. That fool.
So there is only one option left, protect Lilly himself. Peter already told Voldemort where Lily lived, so Severus apparated there, just in time by the looks of James' dead body.
He ran up to the room and avada kedavrad his Lord. Lily looked up in shock, "Severus."
Snape waved, this was awkward, Lilly didn't want him around and he tried to respect that, but this was an emergency! "Hi. I'll leave."
"No!" Lilly ran up to him. "Don't leave. How's James? Is he?"
Snape kept his voice calm, "James was dead when I arrived. I'm sorry." He didn't like James, but he didn't want to hurt Lilly either.
"I, stay here tonight please." To that Harry started crying. "I need a breather."
"Take all the time you need. Give me the baby and I'll handle him." Lilly handed Snape Harry. "Go relax. I'll take good care of him." Lily, shaken, went to take a shower.
Snape looked at Harry, "You look... Just like your father." That was said to a louder cry. "You are right that it is rather unfortunate." Snape went to find Harry a bottle, and fed it to him when he finally found one. That was when he noticed Harry's eyes. "You do have your mother's eyes. They are beautiful."
When Lilly took Harry back Snape asked, "What's his name?"
"Harry. Harry James Potter." Lilly poked Harry's nose. "He looks just like James doesn't he?" Lily sighed, "He'll always be a reminder."
Snape added to the sentence, "A reminder that you survived. Lilly, I am sorry about James. I wish I arrived sooner." He did wish he arrived sooner. Lilly being widowed hurt her emotionally, he can see it.
He didn't care about James and if it didn't hurt Lilly, he would dance on his grave. But he still loved Lilly which means he had to pretend to care about James' death for her sake.
"Severus?" Severus looked at Lilly. "Can you help me with Harry? I can't do it by myself."
Severus smiled, "Of course. I will be better this time Lily, I promise."