One possible plotline could be exploring Snape's internal struggle as he endures Lily's bullying. He might be torn between his feelings for her and the pain she causes. Another could be Lily's realization of her wrongdoings and her journey to make amends.
A great plotline could be set in an alternate universe where Snape decides to stand up to Lily's bullying early on. This changes the dynamics of their relationship completely. It could lead to a series of events where they both grow as characters. Snape might become more confident, and Lily might learn about the consequences of her actions. There could be a point where they actually become friends after working through their issues, which is a very different take from the original story.
Well, in some fanfictions, the plot could focus on how the bullying affects Snape's relationships with others at Hogwarts. Maybe it makes him more withdrawn from his peers, and only a select few understand his situation. It could also show how Lily's actions are a result of peer pressure or her own insecurities.
One possible plotline could be that Lily is forced into betraying Snape due to some dark magic influence on her. Maybe she's under a spell that makes her give away Snape's secrets to his enemies. Another could be that she betrays him out of jealousy. Suppose Snape gets closer to someone else, and Lily, in a fit of envy, does something that seriously harms Snape. It could also be that Lily is misled by false information about Snape being involved in some really bad deeds, and without proper investigation, she believes it and betrays him.
A great plotline might be Snape teaching Lily Luna Potter some of his signature potions in a private tutoring session. Through these interactions, they develop a unique bond. Or perhaps Lily Luna Potter gets into a dangerous situation, and Snape is the only one who can save her because of his in - depth knowledge of the dark arts. This would create a scenario where she has to trust him completely, despite his often - misunderstood reputation.
One common plotline is Snape seeking revenge against the Marauders later in life. This could be through his own dark magic or by using his influence in the wizarding world. Another is Lily trying to mediate between Snape and the Marauders, but often failing as the animosity runs too deep. Sometimes, there's a plotline where the Marauders' bullying of Snape accidentally endangers Lily, which then creates more tension and drama in the story.
One interesting plot could be Snape seeing Lily and James during a Hogwarts event. Maybe it's a Quidditch match and he watches their interactions. He could be filled with a mix of jealousy and longing as he sees James showing off to Lily. Another plot might involve Snape seeing them in a more private moment in the library. He overhears their conversation about their future plans and it makes him realize how much he has lost. There could also be a plot where Snape has a vision of them through a magical object and it haunts him, making him question his own actions and decisions in relation to Lily.
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.
A third plotline could be Snape falling in love during his time as a Death Eater. He meets a witch in Voldemort's inner circle who is also having doubts about their loyalty to the Dark Lord. They bond over their shared misgivings and a desire for something more than the life of a Death Eater. Their love gives Snape the strength to secretly work against Voldemort.
A great plotline could be Snape training Draco in advanced potions and magic that are not part of the regular Hogwarts curriculum. This could lead to Draco having unique skills that help him in the wizarding world. Also, Snape might take Draco on secret excursions to learn about the history of the Dark Arts in a way that doesn't lead him down a dark path but rather makes him understand the dangers better.
Well, in some fanfictions, Snape might be trapped in a magical trap set by Death Eaters who are still loyal to Voldemort's ideals. Harry, with his natural sense of justice and his loyalty to Hogwarts (where Snape also has a complex connection), figures out the trap's mechanism and manages to free Snape. Or perhaps Snape is on the verge of being attacked by a magical creature, and Harry, using his experience with magical creatures from Hagrid's teachings, scares the creature away and saves Snape.
In some fanfictions, Lily confronts Snape when she realizes he has feelings for her that are deeper than just friendship. She might be uncomfortable with this discovery as she sees him more as a friend. So she confronts him to set boundaries. Snape, on the other hand, is heartbroken and this confrontation could change the whole dynamic of their relationship in the fan - created story.
One interesting plotline could be exploring their relationship in their early Hogwarts days more in - depth. Maybe showing how Severus first fell in love with Lily and the little moments they shared in the library or on the grounds. Another could be a what - if scenario where Lily didn't end up with James and Severus had a chance to rekindle their friendship and perhaps more. A third could be a story from Severus' perspective after Lily's death, how his memories of her still haunted and drove him in his actions within the wizarding world.