A plot could be that Harry and Lily are sent back in time by a mysterious spell. In this past time, they discover secrets about the Potter family that were long forgotten. For example, they find out about a hidden magical ability that runs in the family. Lily might use this new knowledge to better protect Harry in their original time. Also, during their time - travel, they could interact with young versions of people they knew in their own time, like a young Snape, and this could lead to some very interesting and emotional encounters.
One interesting plot idea could be that Harry travels back in time and meets Lily before she has him. He could try to prevent her death by warning her about Voldemort. Another could be that Lily time - travels to the future and sees the world after Voldemort's defeat, getting to know the man her son has become. Or perhaps they both travel to a different time altogether, like the time of the founders of Hogwarts, and have to adapt to that era while also dealing with their own relationship and the knowledge they bring from their own times.
One idea could be that Lily travels forward in time and meets Harry as an adult. She gets to see all the good he has done and is filled with pride. Another could be Harry traveling back in time to save Lily from Voldemort, but in doing so, he risks changing the entire future. A third plot idea is that they both get trapped in a time loop together and have to figure out how to break it while also learning more about each other.
One idea could be that Lily Luna travels back in time to the Marauder's era. She could interact with James, Sirius, Remus and Peter, and perhaps change some small events that have a big impact on the future. For example, she might prevent a prank from going too far and in turn, change the relationship dynamics among the group.
One idea could be that the Marauders travel back in time and accidentally change something that affects Lily's future. Maybe they prevent her from meeting James, which then sets off a chain of events to fix the timeline.
One idea could be a story where Harry and Lily Luna Potter time - travel together. They could go back to the time when the Marauders were at Hogwarts and have all sorts of adventures, like helping Sirius and James avoid getting into trouble with Snape. Another plot could involve them facing a new dark wizard threat in the future. Lily Luna could show her own brand of magic, different from Harry's but equally powerful, as they team up to defeat the enemy.
One idea could be that in an alternate universe, Snape manages to save Lily and they both play a big role in Harry's upbringing along with Hermione. Maybe Snape uses his potions expertise and Lily's charm work to create a special protection spell for Harry that Hermione later helps to understand and strengthen. Another plot could be that Lily didn't die but was in hiding, and when Harry enters Hogwarts, Snape has to reconcile his feelings for Lily with his role as a teacher to Harry, while Hermione gets caught in the middle trying to figure out the truth behind their complex relationships.
Another interesting plot could be that they are sent forward in time instead. They have to adapt to the future wizarding world which has changed a great deal. They might be shocked by new magic technologies and different social structures, and their reactions to these changes can make for an engaging story.
One idea could be that Harry travels back in time and tries to prevent Voldemort's first rise to power. He could try to stop Voldemort from creating his first Horcrux, thus changing the entire course of the wizarding war. Another plot could be Voldemort traveling to the future to see how Harry defeated him, and then using that knowledge to change his past strategies. Maybe he would try to find a way to destroy the prophecy before it was made.
A possible plot is that Harry and Tonks time travel to a point where the creation of Horcruxes was just beginning. They could try to stop Voldemort from splitting his soul, which would change the whole course of the wizarding world's history. They would face many challenges, like not being discovered by Voldemort or his followers. Also, Tonks might use her skills to distract or mislead some of the Death Eaters while Harry looks for a way to destroy the Horcrux - making materials or the places where Voldemort hid them.
A great plot might be that Teddy time travels to a time when Harry was a child living with the Dursleys. Teddy could try to secretly protect Harry from some of the bullying and neglect he endured. Or perhaps Harry and Teddy travel to a time long before Hogwarts was founded to learn about the origins of magic in the wizarding world, and they bring that knowledge back to their own time to help improve modern magic.
A more complex plot might be where both Harry and Tom are sent back in time to a point where the Hogwarts founders are still alive. They get involved in the founding events of Hogwarts, and Harry has to stop Tom from influencing the founders in a way that would make Hogwarts more exclusive and dark - sided. Harry could try to work with the founders to see the potential danger in Tom even at a young age.