Snape could be extremely conflicted. On one hand, he may be drawn to the stories out of his unending love for Lily, but on the other, seeing her with James would be like a knife in the heart. He might also be critical of how the fanfiction portrays their relationship, especially if it doesn't align with his own memories and feelings.
He might feel a mix of anger and sadness. Anger because James was often a bully to him, and seeing fanfiction that might depict James and Lily in a positive light could stir up those old resentments. Sadness because he loved Lily deeply and lost her to James.
He might be filled with intense jealousy and pain. Snape has deep feelings for Lily, so seeing her with James would be like a dagger to his heart. He could feel a mix of anger towards James and self - loathing for not being the one with Lily.
Snape's view of James might not change much at first. He has such deep - seated hatred for James due to their past. But if the fanfiction shows James in a more positive or sympathetic light, he may start to question his long - held beliefs about him, just a little bit.
They might be really amused. James could find it funny to see different takes on his family's story. Lily might enjoy seeing new interpretations of the magical world she was a part of. Albus could be intrigued by how others view his father's adventures.
In this type of fanfiction, a plot twist could be that Snape saves them, but they end up having to go into hiding in a completely unexpected place. Maybe they have to live among muggles in a way they never thought possible. Another plot twist could be that Snape saves them, but then realizes that he has put himself in a very dangerous position with Voldemort's followers. So he has to find a way to protect himself while also protecting Lily and James. And there could also be a plot twist where Snape saves them, but they don't believe his motives are pure and they try to escape from him, leading to a whole new set of adventures and challenges.
He could also be shocked into momentary silence. His first sight of Harry might bring back a flood of memories, both good and bad. Maybe he freezes for a second, his mind racing with thoughts of Lily, Harry's mother, and how things could have been different. Then he quickly composes himself and tries to hide his inner turmoil behind his usual stern facade.
Boruto might be in awe. He could see his father in a new light, understanding the struggles and growth Naruto went through. It might also inspire Boruto to better himself and live up to his father's legacy.
One reason could be jealousy. Snape might be jealous of James' popularity and charm. James, on the other hand, could be jealous of Snape's close friendship with Lily in their early years. Another reason is their different personalities. James was outgoing and bold, while Snape was more introverted and brooding. Lily might be attracted to different aspects of each of them, which could lead to the fight as they both compete for her attention.
In many fanfictions, when Snape sees Lily and James, it's a turning point for his character. He could see their relationship as a sign of his own inadequacy, which might initially make him more vengeful. However, as time passes, he might come to understand that his actions are driving Lily further away. This realization could lead to a more complex Snape. He might struggle with his feelings, trying to balance his love for Lily with his dislike for James. Eventually, he might grow to accept their relationship, but still hold a special place in his heart for Lily. This new - found acceptance could make him more empathetic towards others in the long run.
Guilt and redemption can be a theme too. Snape's actions were often driven by his love for Lily and his guilt over her death. Fanfictions may expand on this, showing how he tries to make up for it in different ways. Also, the theme of loyalty - Snape's loyalty to Lily even after her death is a powerful concept that fanfictions often explore, sometimes by creating scenarios where Lily somehow comes back or is still present in a way that tests Snape's loyalty.
Love and jealousy are very common themes. Snape's unrequited love for Lily while she is with James creates a lot of jealousy. It often drives the plot as Snape's actions are influenced by his feelings.