A great fanfiction about Harry Potter's parents' lives is 'James and Lily: Love in the Time of War'. This one could show how they coped with the dark times of Voldemort's rise. It might include their involvement in the Order of the Phoenix, their secret meetings, and how they supported each other. Another fanfic could be 'The Potter Family Legacy' which might trace back the family history and how it influenced James and Lily. And 'Lily Evans: The Girl Who Changed James' could be about how Lily's influence made James into a better person.
One popular fanfiction might be 'The Marauders' Era: The Untold Tales of James and Lily'. It delves into their time at Hogwarts, their friendships, and how their relationship developed. Another could be 'Lily's Secret Journeys' which might explore Lily's life before she met James in more depth, like her family life and her early magical experiences. There's also 'James Potter: The Prankster and the Protector' that could focus on James' growth from a mischievous boy to a responsible father - to - be.
Well, 'The Young Potters' is a fanfiction that might depict their early days together. It could show their first encounters, their initial impressions of each other. There's also 'Behind the Green Eyes: Lily's Story' which could be centered around Lily. It might explore her dreams, her fears, and how she fell in love with James. 'James Potter's Hidden Memories' could be a fanfiction that reveals some untold stories from James' perspective, like his insecurities and how he overcame them for Lily.