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 common theme is forbidden love. Their relationship is not exactly socially acceptable in the context of the world they live in, so many fanfics explore the challenges they face because of this.
One popular Arya Jaime fanfic is 'A Different Path'. It explores an alternate universe where Arya and Jaime meet under different circumstances and form an unlikely alliance. The story is full of interesting character interactions and plot twists.
Imagine if Jaime stayed with Brienne of Tarth! It might have resulted in more emotional depth and character development for both. Maybe they would have formed a powerful alliance and changed the course of events.
Often, Sansa is portrayed as a powerful figure in fanfiction, and Jaime's character can add an interesting dynamic. They might be shown as having conversations that never occurred in the show. For example, Jaime could offer Sansa his insights about the political situation in King's Landing, which she could use to her advantage in her own political maneuvers in the North.
One common theme is redemption. Jaime often has a complex past, and the OC can play a role in his journey towards redemption. For example, the OC might see the good in him when others don't.
I'm not sure specifically what's in 'jaime war stories' as I haven't read it. But war stories usually involve tales of heroism, survival, and the harsh realities of war. Maybe there are stories about soldiers' camaraderie during battles.
The contrast between their characters. Arya is a young, fierce and independent girl with a thirst for vengeance, while Jaime is a complex knight with a troubled past. When combined in fanfics, it creates a lot of potential for unique storylines.
Some fanfictions might focus on a more romantic side. For example, Jaime and the reader could meet in a ball or a gathering. They initially dislike each other but as they are forced to interact more, they start to fall in love. This kind of slow - burn romance is quite common in fanfiction.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a vast collection of fanfictions from various fandoms, and you're likely to find quite a few jaime and reader ones there.