At first, their interaction would likely be very guarded. Sansa would be cautious as she has learned to be in a world full of danger. Tywin would probably see her as a young, naive girl but also a valuable asset. As time goes on, Sansa might start to challenge Tywin's ideas, which could lead to some intense exchanges between them.
Arya and Tywin could also interact in a more unexpected way. Maybe in a situation where they are forced to work together for a short time due to some external threat. During this time, Arya has to constantly remind herself of her ultimate goal of revenge while Tywin is constantly on guard against her, yet also seeing potential in her skills for his own purposes.
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.
One great Arya and Tywin fanfiction is 'The Unlikely Encounter'. It beautifully portrays the first meeting between them and how Arya's quick thinking saves her from Tywin's wrath. Another good one is 'Alliance of Convenience' which explores the idea of them working together against a common enemy. It's full of political intrigue and character development.
In Arya and Tywin fanfiction, their dynamic can be really interesting. Tywin is a shrewd and powerful figure, while Arya is a fierce and determined young girl. One aspect could be a scenario where Arya, in her quest for vengeance, crosses paths with Tywin. Maybe she tries to infiltrate his court or army in disguise. Their interactions would be filled with tension as Tywin would likely see her as a threat, yet be intrigued by her boldness. It could lead to a complex power struggle within the story.
At first, it could be very tense. Tywin is used to being in control and having things his way, and the Stark oc would likely have her own ideas and values. So, they might start off butting heads. But as time goes on, they could start to understand each other better. The Stark oc might see that Tywin has his reasons for his actions, and Tywin could come to respect the Stark oc's strength and integrity.
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.