Well, these fanfictions usually show Snape as a character full of contradictions. On one hand, he has his dark side which is a result of his past and the environment he grew up in. But on the other hand, his love for Lily is so strong that it overrides all that. He is often seen as a tragic hero. He saves Lily not just because he loves her, but also as a way to redeem himself for his past mistakes. His actions in saving Lily are often filled with desperation and determination, which makes his character both fascinating and sympathetic in these fanfictions.
Snape in 'Snape Saves Lily' fanfictions is typically depicted as a hero in a sense. Despite his past associations with the dark side, his love for Lily makes him turn against his former allies. He is shown to be intelligent and resourceful, using his skills in magic, especially his knowledge of potions and dark arts (but using it for good in this case), to save Lily from various threats. He is also portrayed as a very emotional character, his love for Lily being the one pure thing in his otherwise troubled life.
It could end with Lily escaping and being forever angry with Snape. She might cut all ties with him and go on to marry James Potter, with Snape left full of regret for his actions.
In these fanfictions, Snape's character often develops from a seemingly cold and unfeeling person to someone with more depth. When he saves Harry, it starts to chip away at his facade. For example, he might initially save Harry out of obligation but as time goes on, he realizes he has a genuine care for the boy. This is different from his canon behavior where his feelings are mostly hidden.
Often as a complex figure. He's still the reserved and somewhat prickly man we know, but in the context of marriage, his softer side might start to show. For example, he may be more protective of his partner.
Often, Snape is shown as having a more nuanced relationship with Harry. He may not be as cold or harsh as in the original story. Because Harry is the WBWL in a different context, Snape might realize the importance of guiding Harry more quickly. This could lead to him showing more of his true self, his intelligence and his complex emotions, rather than just the surly Potions master.
Snape might be initially in shock. He had trusted Lily deeply, so the betrayal would hit him hard. He could become very angry and bitter, perhaps vowing revenge against her. He might also close himself off emotionally, not wanting to trust anyone again.
In such fanfictions, Lily's forgiveness can make Snape seem more redeemable. It softens his otherwise prickly and often dark character. His actions might be seen in a new light, as if he is now more worthy of understanding and compassion because Lily, who he cared about deeply, has forgiven him.
Snape's character may develop in a way that shows his loyalty to Dumbledore and the greater good in a more obvious way. Saving Harry from Umbridge, who represents the Ministry's overreach and corruption, could be seen as Snape firmly taking a stand on the side of what's right. It could also make him more conflicted internally as he has to balance his role as a double - agent and this new - found 'protector' role of Harry, which in turn would add more depth to his already complex character.
In many of these fanfictions, Snape is often portrayed as a complex and misunderstood figure. He is shown as having a deep - seated sense of loyalty, whether it's to Hogwarts or to the memory of Lily. For example, in some stories, he acts as a sort of guiding spirit for Albus Severus, using his past experiences to help the young Potter navigate the challenges at school.
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.
In these fanfictions, Hermione's character is usually shown as intelligent and resourceful. When she runs into Snape, she uses her wits. Say, if they are in a dangerous situation in a fan - made scenario, she quickly assesses the situation and tries to find solutions, sometimes even suggesting things that Snape hadn't thought of, which makes him view her in a new light.