One possible theme is unrequited love. Snape loved Lily deeply, and their Patronuses, both being doves perhaps in some fanfictions, could symbolize that love. His Patronus could be a constant reminder of his love for her, even though she was with someone else.
In a fanfiction, Snape's Patronus could be the key to saving Lily from a dark magic curse in an alternate universe. Since the Patronus represents love and protection, Snape's doe Patronus might be able to break the curse that has trapped Lily's soul. As he sends his Patronus towards her, it glows with a powerful light that gradually dispels the dark magic surrounding her.
One possible theme is loyalty. Snape's loyalty to Lily was unwavering, and fanfictions can explore how that loyalty manifested in different situations, like when he had to choose between the Death Eaters and protecting Lily. Another theme could be regret, as Snape may have regretted some of his actions that affected his relationship with Lily.
In lily and snape fanfiction, the theme of lost love is very prevalent. Their relationship was cut short, and this sense of loss is often explored. The theme of inner turmoil is also common. Snape's internal struggle between his love for Lily and his association with the Death Eaters is a key element. Additionally, the theme of hope, that perhaps in some way their relationship could have been different, is often seen.
One common theme is unrequited love. Snape's love for Lily was often one - sided, and many fanfictions explore this aspect in depth.
One reason could be jealousy. Maybe Snape gets jealous of Lily's other relationships or her popularity at Hogwarts. Another could be a fundamental difference in their beliefs or values that grows over time into hatred.
It could be that in fanfiction, Snape has been through some additional trauma or experiences that change his perception of Lily. For instance, if he discovers something about Lily that he doesn't like, such as her involvement in some secret or her having a different side to her character that he finds unappealing. This would cause him to dislike her, as opposed to his more nuanced feelings in the original story.
One reason could be jealousy. If in the fanfiction Snape is getting more attention or praise from the wizarding world than Lily, she might start to dislike him. Another reason could be that Snape has a different view on blood purity, and Lily strongly disagrees with him, which leads to her hatred.
It could also be due to some external factors. Maybe there are threats from dark forces that he doesn't want to involve Lily in. If he is getting deeper into the dark arts or some dangerous situations, he might choose to give up on her to protect her from the potential harm that could come her way because of his associations.
Well, it really depends on the fanfiction author's creativity. Some might give her a Patronus that reflects her own unique personality traits. For example, if she's portrayed as very brave and fierce in a particular fanfic, her Patronus could be a lioness, representing her courage and leadership. Another possibility is that it could be a bird, perhaps a phoenix, which would tie in with the magical and powerful nature often associated with the Potter family.
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.