You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions from various fandoms, including those related to Joffrey. There are likely to be many different takes on his character there.
Yes, there are some. You can check out fanfiction websites like Archive of Our Own. There you might find various interpretations of their relationship in the fan-created stories.
Well, there's a fanfiction called 'Sansa's Redemption of Joffrey'. In this story, Sansa tries to influence Joffrey to become a better person. It delves deep into their complex relationship, showing how Sansa's kindness might have the potential to change Joffrey's nature. It's quite an interesting read as it gives a different perspective on their characters compared to the original 'Game of Thrones' narrative.
One popular 'Joffrey and Sansa love fanfiction' is 'A Different Path' which explores an alternate universe where Joffrey is not as cruel and he and Sansa develop a more tender relationship. However, this is quite different from the original storyline in the books and show.
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.
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 Joffrey was good, it would completely change the dynamic of the story. The conflicts and power plays would be very different.
Finding specific fanfiction about Joffrey, Sansa and Lemon can be a bit tricky. Fanfiction.net might also be a place to check. However, keep in mind that the quality can vary greatly. Some fanfictions might focus more on the relationship dynamics between Joffrey and Sansa, while others might use the 'Lemon' aspect in different ways, like as a code name for something in the story or as a symbol related to a particular setting. You really have to dig through the search results to find something that suits your taste.
One great Joffrey Baratheon OC fanfiction is 'The Redemption of Joffrey'. It presents an original character who tries to reform Joffrey. Another is 'Joffrey's Unlikely Ally' which shows how an OC gets involved in Joffrey's court politics in a very interesting way. And 'A Different Joffrey' which gives a new perspective on his character through the eyes of an OC.
Rather than seeking such specific and often unwholesome fanfiction, it's more enjoyable to explore fanfictions that stay true to the essence of the characters. For example, fanfictions that expand on Arya's adventures in Braavos or her training with the Faceless Men. These are much more in line with the spirit of the 'Game of Thrones' universe.