They could time travel to a parallel universe where the roles are reversed. In this universe, Luke is a Sith, Leia is a bounty hunter, and Han is a political leader. They are shocked by these changes but soon realize that they need to find a way back to their own universe. Along the way, they learn about the different choices that led to these alternate identities. Luke sees how easy it was for him to turn to the dark side in this universe, which makes him more determined to stay on the path of the light in his own world.
One idea could be that they travel back to the time before the fall of the Republic. Han could try to use his smuggler skills to prevent certain events that led to the rise of the Empire. Luke might seek to train with the Jedi of that era, and Leia could try to influence galactic politics to avoid the chaos that ensued.
One possible plot could be that Anakin, Padme, Luke and Leia are sent back in time to the Clone Wars era. Anakin could have the chance to prevent his fall to the dark side, with Padme by his side to support him. Luke and Leia would be there to help their father, using the knowledge they have from the future. They could change the course of the war and save many lives, while also ensuring the Sith don't gain so much power.
Well, a possible plotline is that Luke and Leia time travel to the era of the Old Republic. They might meet the Jedi of that time and learn different ways of the Force. Maybe they get involved in an ancient Sith - Jedi conflict, and their presence changes the outcome in unexpected ways. For example, they could introduce new Force techniques they learned from their own time, which could tip the balance of power in that historical struggle.
In time travel situations, they may have to rely on each other in ways they haven't before. For example, if they travel to a time when the Force is not well - understood, Luke may have to depend on Han's non - Force - related skills more. Leia might find herself in situations where she has to mediate between Han and Luke more often, strengthening their bond as a trio. Their relationships would grow deeper as they face new challenges together.
If they time travel, their relationships might become more complex. For example, if they go back in time to before they met, they might initially not trust each other as they do in their own time. Han might be more distrustful of Luke's Jedi abilities, and Leia might not see Han as the hero she knows him to be. But as they face challenges together in the past, they could form deeper bonds in different ways than they did originally.
In this kind of fanfic, a lot could happen. Maybe Anakin could use time travel to prevent his fall to the dark side. He might go back and make different choices, which would then change the entire future for Luke and Leia. Padme could also be involved in this time - traveling adventure. For example, she could use her knowledge of future events to try and save the Republic in a more effective way. And Luke and Leia, they might end up traveling through time as well to learn more about their parents' past and the history of the Jedi and Sith.
Maybe in the fanfic, Padme discovers a time - travel device and decides to use it to go back in time to when Anakin was still a young Jedi. She hopes to change the course of his life and prevent his turn to the dark side. Luke and Leia, sensing something is wrong with the timeline, follow her. Once there, they have to navigate the complex politics and relationships of that era while also trying to keep their true identities a secret. This could lead to all sorts of interesting interactions and plot twists.
There are some fanfictions where the time travel is not just about changing the past, but also about learning from it. For instance, Luke travels back to the time of his father's youth. Instead of trying to directly change Anakin's path, he tries to understand the root causes of his fall. He then takes this knowledge back to his own time to better prepare the Jedi order for future threats. And Leia, when she travels back, might focus on building alliances that could have prevented the rise of the Sith in the first place. This kind of plot adds depth to the characters and the overall Star Wars universe.
One interesting plot could be Luke and Leia traveling back in time to the Clone Wars era. They could try to prevent certain events that led to the rise of the Empire. For example, they might attempt to save Jedi who were wrongly killed. Another plot could be them traveling to the future to see the state of the galaxy after their time and then bringing back knowledge to change their present.
One possible fanfic could be about Anakin using time travel to prevent the fall of the Jedi Order and save Padame. He could then ensure a better future for Luke and Leia, guiding them in the ways of the Force without the dark shadow of the Empire looming over them.