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 some Luke and Leia time travel fanfiction, they might travel back to the time just before Anakin's fall to the dark side. They could try to influence him in a positive way, by showing him the consequences of his future actions. They might also try to prevent Palpatine from manipulating Anakin in the first place. Their relationship as siblings could be a crucial factor in this, as they could offer Anakin the family support he lacked in the original timeline.
A third plotline could be set in an alternate universe where Luke and Leia meet under different circumstances. For example, they could meet as children before they were separated. This would completely change the dynamic of their relationship and lead to a whole new set of adventures and character developments.
One interesting plotline could be Luke and Leia going on a joint mission to discover more about their mother. They might face various challenges along the way, like encountering an ancient Sith artifact that tests their Jedi abilities and their bond as siblings.
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.
Another plotline could involve them traveling to the future. Maybe they see a world where the Jedi have been fully restored and are working in harmony with the galaxy. This could make Vader question his past actions even more, and Luke could gain new insights into the future of the Jedi Order.
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 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.
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.
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.
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.
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.