One possible plot could be a young Lannister male OC who, unlike his power - hungry relatives, is more interested in the arts and knowledge. He could secretly befriend a maester and learn about ancient Valyrian lore. This would put him at odds with his family as they see his pursuits as a waste of time. He might then use his knowledge to try and broker peace during the war, facing many challenges along the way.
The male OC Lannister could be a bastard son of Tywin. He is shunned by most of the family but has a natural talent for strategy. He starts off as a squire for a minor knight. As the War of the Five Kings erupts, he uses his wits to gain a small but loyal following. He then tries to prove himself to the Lannisters by devising clever battle plans. He also has a love interest, a commoner girl who he tries to protect in the chaos of war.
If the male OC Lannister was a proud and ambitious type, he would likely interact with Cersei with a mix of respect and rivalry. He'd try to gain her favor while also making sure she didn't see him as a threat. With Tyrion, he might initially look down on him but later come to respect his intelligence. And when it comes to Jon Snow, he could start off as dismissive but as he realizes Jon's leadership skills, he might try to form an alliance.
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.
Perhaps an OC Lannister who is a talented healer. In a world full of wars and battles in Game of Thrones, a healer Lannister could be an interesting addition. They might have to deal with the moral dilemma of healing both their own family's enemies and allies. They could also have a secret love affair with a member of another house, which would add a layer of drama.
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 of the main themes is family dynamics. The Lannisters have a complex family structure, and the OC has to find his place within it. Also, the theme of survival is prevalent. In the cut - throat world of Game of Thrones, the OC has to fight to stay alive and relevant. And then there's the theme of reputation, as the Lannister name comes with both advantages and burdens.
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.
To develop the male OC, start with his goals. Maybe he wants to gain power and sees Cersei as a means to that end. His appearance can also play a role. If he has a striking look, it might attract Cersei's attention. His relationships with other characters are crucial too. If he has a close friend or mentor, they could influence his actions towards Cersei. For instance, if his mentor warns him about Cersei's dangerous nature, he has to decide whether to listen or pursue his own desires.
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.
The male OC could be a sellsword who is hired to protect Cersei. At first, she looks down on him as a common mercenary, but he proves his worth by saving her life multiple times. This causes her to reevaluate her opinion of him and a relationship begins to develop. Another plot is that the male OC is a noble from a small house who has a unique claim to the throne. Cersei tries to use him for her own political gain, but in the process, they fall in love. And there could be a plot where the male OC is a minstrel, whose songs touch Cersei's heart and make her open up in ways she never has before.
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.