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.
Another plot could be that they keep getting sent to different random time periods. In one time, they end up during a great Jedi - Sith war. Han is out of his depth in this highly Force - sensitive environment. Luke tries to learn from the ancient Jedi, and Leia has to use her diplomatic skills to survive among the warring factions.
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.
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.
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.
In a time travel fanfic, Anakin and Padame could be sent forward in time to meet Luke and Leia. At first, they are shocked by the state of the galaxy. But then, they decide to use their knowledge of the past to help Luke and Leia in their fight against the remnants of the Empire. Anakin, having redeemed himself in this new future, could train Luke further, and Padame could offer diplomatic and strategic advice to Leia.
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.
Another interesting plot is Luke traveling to the future. He discovers a galaxy in chaos due to a new, powerful dark force. He has to adapt to new technologies and new forms of the Force while also finding a way to defeat this new threat. He might meet descendants of his friends and foes, which would add an interesting dynamic.
One idea could be a story where Luke and Leia discover a long - lost Jedi temple together. They have to face ancient traps and puzzles while also dealing with their own growing Force powers. Another plot could be set during a time of peace in the galaxy, and they go on a diplomatic mission to a new planet, facing political intrigue along the way. Maybe a plot where they are forced to team up against a new Sith threat that is targeting them specifically because of their connection to Vader.
A plot might also involve a young Rebel pilot who stumbles upon the hiding place of baby Luke and Leia. Instead of turning them over to the Rebellion right away, he decides to take matters into his own hands and protect them personally. He has to evade both Imperial and some over - eager Rebels who want to use the children as symbols, all while learning about the importance of family along the way.
One idea could be a story that focuses on Anakin and Padame's relationship before the events that led to his fall. It could explore their secret meetings and how they coped with the Jedi Code restrictions. Then, as the story progresses, it could show how their relationship influenced Luke and Leia's upbringing and destinies in a more in - depth way than what we saw in the movies. For example, Padame could have left some hidden teachings or messages for her children that they discover later in life.
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.