Cersei could be the most interesting in a sense. If she were reincarnated, she could either double down on her power - hungry ways or completely change. Maybe she could learn from her past mistakes and become a more benevolent ruler. Or she could use her reincarnation as a way to exact revenge on those who opposed her in her previous life in more devious and calculated ways.
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.
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.
The uniqueness lies in the way it can rewrite Jaime's story. In the original series, Jaime's path is somewhat set. But in this fanfic, the self - insert can change his fate. They might be able to prevent him from making some of his more controversial decisions or push him towards actions that would lead to a completely different outcome for him and the whole of Westeros. It gives a fresh take on the already rich 'Game of Thrones' lore.
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.
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.
In the Game of Thrones novels, Tyrion Lannister remains alive. His character undergoes many challenges and developments but doesn't meet his end. The author has kept him as an important part of the ongoing narrative.
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.