One interesting plot could be Lily's struggle with her identity. Being the daughter of Voldemort, she might constantly battle between the dark side that is in her blood and the good she has been taught. For example, she could be tempted by dark magic but resist it because of the friends she has made at Hogwarts.
Another plot could involve Lily trying to redeem the name of her father. She might believe that there was some good in Voldemort deep down and attempt to change the wizarding world's view of him. However, this would put her at odds with many people who have suffered at his hands.
In the fanfiction, Lily would likely face a great deal of prejudice. The wizarding world would be very suspicious of her because of who her father is. This is different from the original Lily who was respected and loved. So, she would have to work hard to prove herself, which could lead to a more complex and hardened personality compared to the original.
In some stories, their friendship could start from a time - travel accident. Harry gets sent back in time and ends up befriending a young Voldemort. He tries to influence Voldemort's path, and they form an unlikely bond. Harry might introduce Voldemort to different values and ideas that were not present in Voldemort's original upbringing, which causes a major shift in the future of the wizarding world.
One interesting plot could be that they are distant relatives through some ancient wizarding bloodline. Maybe there was a curse placed on the family long ago that led to their enmity.
One possible plot could be that Voldemort's daughter is actually a good - hearted person despite her father's evil. She meets Hermione and they initially clash due to their different backgrounds. But as time goes on, they discover they both have a love for knowledge. Hermione helps her break away from the shadow of her father's name and they become friends, fighting against the remaining Death Eaters who want to use the daughter for their own evil plans.
One possible plot could be that Voldemort's curse backfires in a different way. Instead of killing them, it transports Lily and James to a parallel magical dimension. In this dimension, they are able to secretly raise Harry while still being alive. They could then use their knowledge of the future to train Harry more effectively and build a stronger resistance against Voldemort. Another plot might involve a powerful magical object that they discover which has the power to protect them from death spells. They could then use this object to not only save themselves but also to help the wizarding world in the fight against the Dark Lord.
Another plot could involve a time - travel scenario. Lily Potter travels back in time and encounters a younger Albus Dumbledore. Their ideologies clash as Lily, coming from a different era, has different views on how magic should be used and how the wizarding world should be run. This could lead to a series of events where they have to either work together or oppose each other depending on the situation.
One possible plotline could be the daughter of Voldemort struggling with her identity. She might be torn between her father's dark legacy and the potential for good that she sees in the wizarding world. Another could be her forming an unexpected alliance with Harry Potter, perhaps to atone for her father's sins or to find a new path for herself.
One interesting plot could be that they travel back to the time of the Marauders. James and Lily could meet their parents when they were young and see how different Hogwarts was back then. They might get involved in some of the Marauders' pranks and also learn some secrets about their family's past that were long forgotten.
One interesting plot could be Lily traveling back in time to prevent James and Sirius from playing a particularly dangerous prank that had unforeseen consequences. Another might be Harry traveling back to meet his mother as a young witch and getting to know her in a whole new way. And perhaps Lily and Harry traveling back together to change certain events that led to the rise of Voldemort, like preventing the first opening of the Chamber of Secrets.
One interesting plot could be how Harry and Voldemort initially react to the betrothal. Maybe Harry is completely shocked and disgusted at first, while Voldemort sees it as a way to further control the wizarding world through Harry. Another plot point might be how the wizarding community reacts. Some might be horrified, thinking it's a dark and twisted union, while others might see it as a potential way to end the long - standing conflict between good and evil.