Sansa Stark is frequently in these fanfictions. As someone who was a victim of Joffrey's cruelty, if he is in a time loop, Sansa might find herself in a different situation each time. Maybe in one loop Joffrey starts to treat her better, which would completely change her perspective and her own actions within the story. Also, Cersei Lannister could be involved. As Joffrey's mother, she would be very concerned about any changes in her son during the time loop and might try to interfere to keep things as she wants them.
If Arya killed Joffrey in a fanfic, one possibility is that she would become an instant target for the Lannisters. They would stop at nothing to avenge Joffrey's death. Arya would have to go into deeper hiding or rely on her Faceless Men training even more. Maybe she'd have to flee across the Narrow Sea and start a new life in Essos, constantly looking over her shoulder for Lannister assassins.
In some fanfiction, it might be Varys. He was known for his intelligence network and his ability to work from the shadows. He could have seen Joffrey as a threat to the stability of the Seven Kingdoms. So, he arranged for the young king's death, perhaps thinking that a more malleable ruler could take his place and be more easily influenced to make better decisions for the realm.
Obviously, Joffrey is one of the main characters, even though it's a reborn version of him. And then there are usually the other key players in the Game of Thrones world like Tyrion, Cersei as his mother, and Sansa who was his betrothed in the original story. They play important roles in the fanfiction as the reborn Joffrey interacts with them in different ways.
Well, clearly Joffrey is one of the main characters. His brother, depending on the specific fanfiction, could be any of the other male siblings in the story's universe. It could be a brother who is more kind - hearted and has to deal with Joffrey's difficult personality.
In fanfic, the relationship between Joffrey and Sansa is often a complex and twisted one. Joffrey was cruel in the original story, but in some fanfics, writers might explore a different side of him in relation to Sansa. It could be an exploration of what might have been if Joffrey had not been so evil, perhaps delving into a more romantic or at least a more nuanced connection between them.
In a fanfiction, the lemon could play a magical role. Imagine Joffrey is cursed, and the only way to break the curse is through a lemon - related task. This could lead to a whole new side of Joffrey being explored as he has to rely on something as simple as a lemon to save himself.
In fanfiction, a smart Joffrey often has strategic thinking. He's able to plan ahead and manipulate situations to his advantage, much like a chess player. For example, he might outwit his enemies in court politics.