One possible plot could be that James and Lily had a huge argument over James' reckless behavior in a Quidditch match where he took unnecessary risks. After a few days of not talking, James realizes his mistake and arranges a special date for Lily at the Hogwarts grounds. He sets up a picnic under a charmed tree with all of Lily's favorite foods. Lily is initially hesitant but then decides to give him a chance. They start talking, James sincerely apologizes, and they end up sharing their feelings more deeply than ever before, strengthening their relationship.
They could have had a fight because James was jealous of Lily spending time with another boy in their study group. But then James discovers that the boy was just asking Lily for help with a difficult spell. James feels bad for overreacting. He writes Lily a heartfelt letter and sends it to her with a bouquet of magical flowers. Lily reads the letter and is touched. She meets James in the library, and they talk it out. In the process, they realize how much they care for each other and make up.
In such a fanfic, perhaps a villain manipulates time and alters the memories of James and Lily. They might be living in a different reality where Harry doesn't exist in their minds. Harry could then embark on a journey to find the source of this alteration and restore his parents' memories. He could encounter various allies and enemies along the way, all while trying to come to terms with his parents' current state.
One possibility could be that Lily uses some kind of magic, perhaps a very powerful and rare spell. Maybe she does it out of a sense of protecting James from the pain associated with Harry. In the fanfic, it could lead to a lot of confusion for James. He might start a new life without the knowledge of his son, and then as the story unfolds, there could be a series of events that slowly make him start to remember bits and pieces. For example, he might encounter people or objects that were related to Harry, which would trigger his subconscious.
It could be a story that focuses on the relationship between James and Lily through their portraits. Maybe it shows how their love story is remembered and revered in the wizarding world even after their death.
The plot could involve James and Lily giving Harry away to a powerful wizard who has the ability to hide Harry's magical signature completely. This wizard is an old acquaintance of Dumbledore, and they believe that under his care, Harry will be safe from Voldemort's clutches. They sacrifice their parental rights to ensure Harry's safety.
One possible reason could be that he realizes his feelings are unrequited. In the fanfiction, perhaps Lily has made it clear she doesn't have the same feelings for James, so he gives up. Another reason might be external factors. For example, there could be some sort of danger or situation that makes James think he needs to step back from Lily for her own good.
Well, it could be that James and Lily are brought back through some magical time - turning spell. They meet Harry as he is now, a young hero. Harry gets to show them all he has achieved, and they are filled with pride. They might also help him solve some new, unexpected magical problem together.
Well, one possible plot could be that they face a lot of challenges. Their friends might be shocked at first. They'd have to deal with their studies while also preparing for a baby. And they might worry about how the Hogwarts faculty would react, whether they'd be allowed to stay in school.
Maybe it could be a time - travel plot where Ginny somehow gets to meet James and Lily Potter. For example, she could use a magical object or spell that sends her back in time. And then she might have adventures with them, perhaps helping them in some way that also has an impact on the future she came from.
It could be that Lily publicly embarrasses James in front of their friends. She might disclose some of his insecurities that he thought were private, like his fear of not living up to his family's reputation. This would deeply wound James' feelings and cause a rift between them.
There's also 'Lily's Journal'. This fanfic gives a unique perspective as it's told from Lily's point of view. It delves deep into her feelings for James, from initial dislike to growing love, and how she copes with the events around her.