Well, Jaime Lannister had a complex relationship with the Mad King. The Mad King's madness grew over time. He became paranoid and was willing to do extreme things like using wildfire to destroy King's Landing. Jaime, who had sworn an oath to protect the king, saw that the king had gone too far. So, in a moment of decision, he killed the Mad King. This act defined Jaime's character in many ways and had far - reaching consequences for the Seven Kingdoms.
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.
Sure, many fanfiction authors like to play around with different character combinations and scenarios. Jaime Lannister is a complex character, and Lyanna has her own allure in the story. The idea of her being pregnant in a fanfiction involving Jaime could be used to explore themes like love, honor, and the consequences of actions. It might show how these two characters from different houses and storylines interact in such a situation.
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.
It depends on the specific 'Lannister Love Story'. But likely, characters like Jaime Lannister, Cersei Lannister, and Tyrion Lannister could be main characters. Jaime is a complex character with his own set of values and relationships. Cersei is power - hungry and her relationships are often full of manipulation. Tyrion is the outcast in the family and his love life would be interesting to explore in the context of a love story.
There are several good ones. 'Tywin's Ascent' is a fanfic that details his rise to power. It gives a lot of background on his family and the challenges he overcame. 'The Mind of Tywin' is really interesting as it tries to get into his thought process. It shows how he made decisions that shaped the Westeros we know. And 'Tywin's Last Stand' is a fanfic that imagines his final days in a very creative way.
Power is a very common theme. Since Tywin is all about power in the original story, fanfictions often explore how he gains, maintains, or loses power in different scenarios. Family dynamics is another one. His relationship with his children, especially Tyrion, Jaime, and Cersei, is always a rich area for exploration in fanfictions.
Tyrion Lannister was married to Sansa Stark. It was a union that was arranged for political gain. Sansa was a young girl who had already endured much trauma, and this marriage was another blow. Tyrion, on the other hand, was a complex character. He had a sense of justice and kindness that set him apart from his family, but he was still a Lannister. Their marriage was a strange mix of mutual understanding in some aspects and complete incompatibility in others. As the political situation in Westeros became more volatile, their relationship became even more strained, and ultimately, they went their separate ways.