Yes, there are quite a few. You can start by looking on platforms like Archive of Our Own. Some fanfictions in this category explore how her survival would change the entire Harry Potter storyline, with her being able to directly influence Harry's upbringing and the fight against Voldemort.
One common theme is family. Since Lily survives, the Potter family dynamic changes completely. Another theme is the alteration of the war against Voldemort. With Lily alive, she could be a major force in the fight.
Harry's character development would be significantly different. With his parents alive, he would be exposed to a more stable family environment. His magical education could start earlier and be more comprehensive as he learns from two powerful wizards. This could make him more powerful and less impulsive. Instead of seeking validation from others like he did at Hogwarts in the original story, he would have the unconditional love of his parents, which could shape him into a more well - rounded and less angst - ridden character. For example, he might not have had such a strong urge to prove himself in dangerous situations.
One possible plotline could be that Voldemort's attack on the Potter family fails in a different way. Maybe James uses a powerful, unknown spell that deflects Voldemort's killing curse. As a result, Lily and James go into hiding with Harry. They might then start to form an underground resistance against Voldemort, using their knowledge of the Dark Lord's weaknesses. This could lead to a completely different wizarding war, with the Potters at the forefront, and Harry growing up with his parents by his side, learning magic from them directly.
In some fanfictions, if they survived, they might have changed the whole course of the wizarding war. They could have joined forces with other powerful wizards and witches earlier and potentially prevented Voldemort from gaining as much power as he did in the original story. They might have also influenced the Hogwarts curriculum, emphasizing more on defensive magic against the Dark Arts from an earlier stage.
The relationship between Harry and his parents would be completely different. He would grow up with their love and guidance, rather than feeling like an orphan. There would be a much stronger family bond.
One possible fanfiction could be about Lily Potter's ghost guiding Harry in a more direct way than in the original books. Maybe she appears to him during his toughest times at Hogwarts, like when he's facing Voldemort in the Chamber of Secrets, and gives him some special advice or magic that only a mother could pass on.
A possible fanfiction could involve Lily Luna Potter and her time - traveling adventures. She accidentally stumbles upon a time - turning device and gets sent back to the time of the first Wizarding War. There, she has to be careful not to disrupt the timeline while also trying to learn from the events of that time to prevent a similar future catastrophe.
There are fanfictions that rewrite the story from Lily's point of view. In these, we get to see all the major events in the Harry Potter series through her eyes. It's really interesting as we can understand her thoughts and feelings during key moments like when she was facing Voldemort. This gives a fresh look at the familiar story.
One popular type of Lily Potter fanfiction might focus on her time at Hogwarts before she met James. It could explore her friendships, her studies, and how she dealt with the challenges of being a young witch in a magical school. For example, a story could show her in her Potions class, working hard to master difficult spells and potions, and forming a study group with her closest friends.