Often, Lelouch time travels with a code in fanfiction to save someone he cares about or to establish a different order in the world. It might also be to gain more power or knowledge.
It could be when he's trying to correct past mistakes or prevent a catastrophe. Maybe he wants to change the outcome of a major event.
There is a fanfic called 'Lelouch's Time Travel Adventure'. In it, Lelouch travels back in time to a point before the start of the series. He uses his knowledge of the future to try and prevent the events that led to the sad state of the world in the original story. It has some really cool moments where he outsmarts his enemies using future knowledge, and the way the author writes his internal monologues is very interesting, making it a great read for Code Geass fans.
Time travel can greatly expand Lelouch's character development. When he travels back in time, he gets a second chance. This makes him more cautious as he doesn't want to repeat the same mistakes. For example, he might be more careful in his relationships with Suzaku and others, knowing how things turned out before.
One common theme is redemption. Since she's traveling back in time, the female Lelouch often tries to right the wrongs she did in the original timeline. Another theme is the exploration of different relationships. For instance, how her relationships with other characters change when she has the knowledge of the future.
Lelouch's character would likely become more cautious. Knowing the consequences of his past actions through time travel, he might think twice before making rash decisions. For example, he might not be as quick to use his Geass power without considering all the long - term effects.
Perhaps they travel to a time when the Geass power was first created. Lelouch could try to change the nature of the Geass power to make it less destructive. This would involve him interacting with the original creators of Geass and trying to persuade them to modify it. Meanwhile, Nunnally could be learning about the history of their world from a different perspective, which would help them in their future plans.
There's also 'Female Lelouch: Time's Redemption'. In this fanfiction, the female Lelouch's time travel leads to some really unexpected alliances. For example, she teams up with some characters that were previously her enemies in the original timeline. It's full of plot twists and turns.
Another scenario could be a goodbye kiss. If Lelouch has to embark on a very dangerous mission where he may not return. Kallen, realizing she may never see him again, impulsively kisses him. It would be a bittersweet moment filled with unspoken words and the weight of their relationship and the situation at large.
Another theme is the alteration of fate. Since he has the power of time travel, he can change the pre - determined paths of characters and events. This can lead to a whole new set of political and social situations in the story. It's really fascinating to see how the writers play with the idea of destiny.
One great fem Lelouch time travel fanfiction is 'The Time - Traveling Empress'. It has an interesting plot where fem Lelouch uses her knowledge from the future to change the course of the story in a really engaging way.
One possible fanfiction could involve Lelouch traveling back in time and trying to change his relationship with Cornelia Nonette. Maybe he uses his knowledge from the future to prevent certain events that led to their conflict. For example, he could try to find a way to make her understand his motives earlier in the story, which might lead to an alliance between them instead of enmity.