Well, a cool plot could be that Arya, while on her journey of revenge, stumbles upon a situation where she has to save Tywin's life for some reason. This creates a complex relationship between them. Maybe Tywin then feels indebted to her and tries to offer her things in return, like a pardon or a position in the Lannister court, which Arya has to decide whether to accept or not. Also, a plot could involve a magical element where Arya and Tywin are both affected by some ancient magic that binds their fates together, forcing them to work together despite their hatred for each other's houses.
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.
A possible plot in the fanfiction could be that Arya, after her training with the Faceless Men, targets Tywin as her next victim. But as she gets closer to him, she realizes that he is not as one - dimensional as she thought. There are political intrigues and family issues within the Lannisters that she starts to understand. Meanwhile, Tywin becomes aware of a strange presence around him, not knowing it's Arya. This leads to a cat - and - mouse game between them, filled with suspense and unexpected revelations about both characters.
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.
Maybe in the fan fiction, Tywin discovers Arya's true identity but decides not to kill her immediately. Instead, he tries to use her as a pawn against the Starks. He might try to train her in the Lannister ways, which would put Arya in a difficult position of having to resist while also trying to find a way to outwit Tywin.
Well, in some fanfictions, Sansa might learn from Tywin about power and leadership. Since Tywin is a master of political intrigue, Sansa could start to pick up on his strategies. For example, she could use his teachings to gain more influence in the court, while also trying to keep her Stark identity intact. This would create an interesting dynamic between them as she tries to navigate the dangerous world of the Lannisters.
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 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 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.
Their relationship could develop in a very complex way. At first, Arya would be full of rage towards Tywin. However, if she were to be captured by the Lannisters and Tywin were to show her a different side of himself, perhaps a more paternal side (even if it's just a ploy), Arya might start to question her hatred. On the other hand, Tywin might see Arya as a potential asset, someone he could mold in his own image. This could lead to a relationship that is part mentor - mentee and part captor - captive, with a lot of power dynamics and emotional turmoil.
One plot idea could be that Arya, in her guise as a servant in King's Landing, catches Tywin's attention not for her identity but for her sharp intellect. Tywin, always on the lookout for useful tools, begins to test Arya in subtle ways. For example, he might ask her opinion on various political matters in a veiled attempt to see if she has any insights that could be of use to him. Another idea is that Arya, while still hating the Lannisters, realizes she can use Tywin to gain access to information that could help her in her long - term revenge plans. She has to balance her hatred and her need for secrecy while Tywin remains oblivious to her true nature.
Often, there's a plotline where the OC is a servant or a low - born character who rises to prominence and has to deal with the politics of Tywin Lannister and the Starks. They might be caught in a web of lies and intrigue as they try to serve both sides without getting killed. Also, a plotline could involve an OC as a mage or a seer who foresees the destruction that the feud between the two houses will bring and tries to stop it.
One plot idea could be Arya and Jon teaming up to uncover a long - hidden family secret. Maybe there's a lost Stark heirloom that has some sort of power, and they have to go on a quest to find it. Another idea is that they are both sent on a diplomatic mission to an unfriendly kingdom, and they have to use their unique skills - Arya's stealth and Jon's leadership - to succeed.