What could be the motivation for Snape to save Harry from Vernon in the fan fiction?

In this fan fiction scenario, Snape might use his knowledge of the Muggle world and Vernon's weaknesses. Snape could have found out some information about Vernon's business affairs or personal secrets. Then he blackmails Vernon into leaving Harry alone. By doing this, he effectively saves Harry from Vernon without having to use too much magic and draw unwanted attention.

Love for Lily. Since Harry is Lily's son, Snape might feel an obligation to protect him. He couldn't save Lily, but he can try to keep her son safe.

In this type of fanfiction, Snape could simply intimidate Vernon. Snape has an air of mystery and a certain power about him. He might show up at Vernon's doorstep, give Vernon a cold stare, and with his reputation as a powerful wizard, Vernon might be too scared to oppose him. Snape could then just take Harry without much resistance from Vernon.

One motivation could be Snape's sense of duty as a teacher. Despite his dislike for Harry in some ways, he still has an obligation to protect the students. So, when he sees Lockhart endangering Harry, he steps in.

If Snape witnesses Vernon abusing Harry in fan fiction, he might use it as an opportunity to gain some leverage over Harry. Snape could offer to keep quiet about the abuse in exchange for Harry doing certain things for him, like getting good grades in Potions. However, this is a rather cynical view and goes against Snape's more complex character who deep down has some good in him.

Snape might do it out of his love for Lily. Since Harry is Lily's son, he feels a sense of obligation to protect him.

It could be Sirius Black. Sirius is Harry's godfather and he is very protective of Harry. He might break out of his confinement (if he is still in that situation in the fan fiction) and rush to Vernon's house. Sirius has the skills and the determination to face Vernon and save Harry. He could transform into his Animagus form, a large black dog, and intimidate Vernon into letting Harry go.

One motivation could be simple friendship. Despite being from different schools, they might have developed a bond during the Tri - Wizard Tournament. Viktor could see Harry as a worthy opponent and not want to see him die in the second task.

Maybe Dumbledore steps in at the last moment and takes Harry away from Vernon's house. He could use his powerful magic to protect Harry and remove him from that hostile environment.

Perhaps he realizes that Harry has potential that can be used for his own purposes rather than just killing him. So he wants to keep Harry close and away from the Dursleys who are just muggles.