A fanfic could explore a scenario where the values of the Naruto universe, like friendship and hard work, clash with the more cut - throat and power - hungry values of the Lannisters. This could lead to interesting character developments as characters from both worlds try to understand each other.
One idea could be that the reincarnated Lannister has all the memories of their past life. They could use this knowledge to avoid the mistakes their previous self made. For example, not getting involved in certain political schemes that led to their downfall. Another plot could be that they try to change the fate of their family members. Maybe prevent Jaime from losing his hand or stop Cersei from going down her tyrannical path.
A plot could involve a time - travel scenario. Ned Stark somehow travels to a time when Cersei was younger and more vulnerable. Instead of seeing her as the enemy, he tries to guide her in a different path, which could lead to a completely different political landscape in Westeros. This would involve a lot of character development for Cersei as she grapples with this new perspective from Ned.
An interesting plot idea for Naruto fanfic might be to focus on the life of a minor character. For instance, what if we told the story of a genin who never made it to be a chunin but still had a significant impact on the village in some other way? Or a story where all the ninja abilities are suddenly switched among the characters, and they have to adapt to these new powers while still facing their usual enemies. This could lead to some really fun and unexpected character interactions.
One plot idea could be an OC who is a healer and tries to cure Cersei of a mysterious illness that no one else can figure out. This could lead to a complex relationship between them as Cersei is not used to depending on others.
One idea could be a political alliance. Rhaella, being a Targaryen, and Tywin, a powerful Lannister, could form an uneasy alliance to deal with a common threat to the Seven Kingdoms. They might start off distrustful of each other but gradually come to respect one another's political acumen.
One plot idea could be that Tywin, seeing Sansa's value as a political pawn, decides to use her in a different way than originally planned. Instead of marrying her off to Tyrion, he takes her under his wing to teach her the ways of politics in Westeros. This could lead to an unlikely bond between them as Sansa tries to navigate the dangerous world of the Lannisters while still holding onto her Stark identity.
One possible plot idea could be a Lannister character traveling to Taiwan - like setting in the Game of Thrones world and having to adapt to a different culture and political landscape there. Maybe they form alliances or face new enemies.
One idea could be the daughter getting involved in the political intrigues of King's Landing. Maybe she has to navigate the complex relationships between the different houses while trying to uphold the Lannister name. Another could be her having a secret talent, like being an excellent strategist, which she uses to help her father in unexpected ways.
One plot idea could be Arya, in disguise, getting close to Tywin as a servant in King's Landing. She could overhear his plans and use that knowledge to try and undermine the Lannisters from within. Another could be a scenario where Tywin discovers Arya's true identity but decides to keep her alive for some strategic reason, perhaps to use her as a bargaining chip against the Starks. And a third idea might be a story set in an alternate universe where Arya and Tywin form an unlikely alliance against a common, greater threat, like a White Walker invasion in the south before the events at the Wall.
One idea could be the OC's struggle to live up to his father's reputation. He might face challenges within the Lannister family, like dealing with his siblings' envy or rivalry. Another could be his role in the political games of Westeros, perhaps trying to form alliances different from his father's.