It deteriorates rapidly. Lily is likely to be extremely hurt and angry. She probably won't be able to forgive Snape easily, if at all. Their relationship which might have had some complexity and depth before, turns into one of animosity from Lily's side.
The relationship becomes very strained. Snape may realize his mistake too late. Lily could start to view Snape as just another bigot in the wizarding world. She might distance herself not only from Snape but also from any of his associated groups or ideas. This change could be a turning point in the fanfiction's plot, leading to different paths for both characters.
On the other hand, it could also lead to a strange kind of understanding. Maybe Harry realizes that Snape is under a great deal of pressure and that the punch was a momentary lapse. This could make Harry more empathetic towards Snape, although he might still be angry about being punched.
It would strain their relationship even more. Snape's love for Lily was already on shaky ground due to their different paths. Seeing her with James would make him feel like she has completely chosen the other side, and he might start to resent her a bit.
The relationship could become more complex. On one hand, Snape would feel a stronger sense of obligation to protect Lily. This might make Lily feel a bit smothered. On the other hand, she would be grateful for his protection during the attack. But she might also be conflicted because she was friends with some of the Marauders too. This could lead to some tension between her and Snape as they deal with their different views on the Marauders.
In fanfiction, one possible consequence could be a complete breakdown of their friendship. Lily might cut all ties with Snape immediately. This event could also lead to Snape's further isolation at Hogwarts as Lily was one of the few people who had some sort of positive connection with him. Moreover, it could fuel Snape's inner turmoil and his journey towards either redemption or further descent into the dark arts, depending on how the author of the fanfiction chooses to develop his character.
Often, fanfiction will explore the idea of Lily having a deeper understanding of Snape's actions and motives. This can lead to a relationship where she is more forgiving and empathetic towards him. For instance, in some stories, when Snape is bullied, Lily steps in more actively to defend him, which changes the dynamic of their relationship. In other cases, the relationship might be reimagined in a romantic way that was only hinted at in the original. There could be a scenario where they actually start a relationship during their Hogwarts years, which would completely change the course of their individual lives and how they interact with other characters like James Potter.
The story might take a more somber turn. Snape could become more withdrawn and focus solely on his own pursuits. For instance, he may throw himself into his potions research even more intensely.
In the fanfiction, Snape's impression might make him more protective of Harry. He could start to subtly look out for Harry's well - being, whether it's in the face of other students' bullying or more dangerous threats from the dark side. This would be a significant change from their usually strained relationship in the original story.
At first, it's likely to be tense. Harry has years of seeing Snape as a bully. But as they start living together, they begin to understand each other. Snape might show his more vulnerable side to Harry, like his memories of Harry's mother. Harry, in turn, starts to respect Snape's knowledge and sacrifice. Eventually, they develop a bond like a father - son relationship.
It could completely shatter their relationship at first. Hermione, being proud and intelligent, wouldn't tolerate such an insult easily. Their friendship might seem irreparable. However, if the story is about growth and redemption, Harry would have to go through a lot of self - reflection. He'd need to understand the depth of his wrong and work towards winning back Hermione's trust, perhaps by standing up against those with discriminatory views more actively in the story.
A love potion can turn their relationship upside down. Harry, normally having a somewhat adversarial relationship with Snape, would suddenly be filled with love for him. This could lead Snape to question his own feelings towards Harry. He might start to see Harry in a new light, perhaps noticing his positive qualities more. And for Harry, he might start to understand Snape better as he pursues this new - found love, even if it's not real in the beginning.