Their relationship might become more complex. Since they'd be in a different time, they might rely on each other more. In their own time, they had different paths, but going back in time could force them to be closer. They might start to see each other in a new light, like Luke seeing Leia as more of a partner in adventure rather than just a sister.
One possible plotline could be that Luke and Leia go back in time to prevent the rise of the Empire. They might try to stop key events like the corruption of Anakin Skywalker. For example, they could warn the Jedi Council about Palpatine's true nature. Another plotline could be that they go back to save their mother. They would have to figure out how to do this without changing too much of the future. Maybe they'd work with young Obi - Wan Kenobi.
Well, they might prevent some great tragedies in the Star Wars universe. For example, they could stop Anakin from turning to the Dark Side. This would completely change the course of history in the galaxy.
Often, Palpatine can still be a main antagonist even in time travel fanfiction. If Luke and Leia travel back in time, he might sense their presence and try to stop them from changing things that would undermine his power. Another could be Darth Vader if they travel to a time when he was still firmly on the dark side. He would be a powerful foe for them to face.
The relationship would likely be more sibling - like from the start. In the original story, they didn't know they were siblings for a long time. But in this fanfiction, they'd grow up with that knowledge. So, they'd be more protective of each other right away and have a deeper understanding of each other's quirks and abilities.
One possible scenario is that they travel to a planet where they believe their parents' spirits reside. They might face various challenges on their journey, like hostile creatures or difficult terrains. Along the way, they could discover more about their family's history through ancient artifacts or wise beings.
I really liked 'The Time - Traveling Skywalkers'. It's a story where all four characters are caught in a time - travel anomaly. They end up in different points in time relative to each other. Padme gets to see a future where her children have grown up strong despite all the hardships. Anakin has to face his past self and tries to guide him away from the dark side. Luke and Leia use their knowledge of the future to try and make the galaxy a better place in the past. It's a really engaging read.
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.
The Sith, of course. Even in the past, the Sith would be a major threat. They might try to stop Luke and Rey from changing things that would be detrimental to their plans for galactic domination.
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.