Well, 'Lannister in Exile' is a good one. It tells the story of a Lannister who has been exiled from Westeros and must find a way to survive and regain his family's honor in a foreign land. Another interesting fanfiction is 'The Lannister Heir'. This one focuses on an unexpected heir in the Lannister line and the power struggles that ensue within the family as a result.
One great 'OC Son of Lannister' fanfic is 'The Lannister's Heir'. It explores the journey of the OC as he tries to navigate the complex politics of Westeros. Another is 'A Lannister's Redemption' which shows how the character battles with the family's reputation.
There could be a fanfiction that focuses on an alternate universe where Tywin survives longer. In this story, he would have to deal with the changing political landscape after the events at King's Landing. He might try to regain control of the situation, perhaps by making alliances with unexpected parties. His character would be forced to adapt to new threats and challenges, which could lead to some very interesting plot developments.
If Naruto was a Lannister in a Game of Thrones fanfiction, he'd be a very different kind of Lannister. He'd probably use his ninja skills to protect the family in ways they've never seen before. Instead of the usual backstabbing, he might bring in a sense of loyalty and honor that the Lannisters lack. He could use his jutsu to make the Lannister stronghold more secure, like creating barriers with his earth - style jutsu.
One plot idea could be that your self - inserted character is a Lannister bastard who is trying to prove their worth to the family. Another is that your character discovers a long - lost Lannister treasure and has to fight off other family members who want it for themselves. Or perhaps your character is a Lannister who has a secret alliance with a rival house and is trying to bring down the main Lannister power from within.
One great 'Game of Thrones Tywin Lannister Fanfiction' is 'The Lion's Legacy'. It delves deep into Tywin's past, showing his rise to power in a very detailed and engaging way. The author does an excellent job of portraying his complex personality.
I really liked 'Jaime Lannister: A Different Path'. In this fanfiction, Jaime decides to side with the Starks early on. It's an interesting take as it completely changes the course of his character in a believable way. There are some great character interactions that are not in the original show.
Power is a very common theme. The Lannisters are known for their lust for power in the original series, and fanfictions often explore how they gain, maintain, or lose power. Family loyalty is another. Despite their many flaws, the Lannisters have a strong sense of family loyalty, and this is often a central theme in fanfictions.
Some fanfictions have Jaime exploring the Free Cities. This is different from his usual Westerosi setting in the show. He gets involved in different cultures and politics there, which makes for an exciting read as we see how he adapts.
Consider their upbringing. If they were raised away from the main Lannister stronghold, they might have a different set of values. Maybe they were raised by a kind - hearted servant who taught them to be more empathetic. So their personality could be a mix of Lannister pride and this new - found empathy. They could be conflicted between loyalty to their family and doing what is right according to their own conscience.
Another place could be Wattpad. There are many fanfiction writers on there who might have written something about the Lannisters in the context of Game of Thrones. However, it may take some time to sift through the numerous works to find specifically what you're looking for regarding Taiwan and the Lannisters.