It's not appropriate. The original Avatar: The Last Airbender series is aimed at a wide audience, including younger viewers. 'Lemon' fanfiction often contains adult - themed content. Katara and Ozai have a relationship in the show that is based on enmity and conflict. Turning this into a sexualized relationship in fanfiction is a misrepresentation of the characters and the story, and is not suitable for the general Avatar fan community.
One great 'Zuko and Katara Fanfiction' is 'The Phoenix and the Wave'. It beautifully explores their relationship development. The story is set in a post - war scenario where they have to work together on a diplomatic mission. Their initial distrust slowly turns into mutual respect and something more.
Well, a common theme in fanfiction is their romantic adventures. Fanfic writers love to imagine Aang and Katara going on secret dates to beautiful, hidden places. These could be secluded islands or magical caves. Their relationship in fanfiction can also be a bit more complex than in the original series. There could be misunderstandings due to their different upbringings. Aang being the last Airbender with a more carefree nature at times, and Katara being a strong - willed Water Tribe girl.
In some cases, the anger could be a catalyst for a more romantic development. Aang expressing his strong emotions might make Katara realize the depth of his feelings for her. Or it could be the other way around, Katara's reaction to his anger could make Aang see her in a new light, leading to a shift in their relationship dynamic towards a more romantic one.
Friendship is also a big theme. Katara often forms new friendships in the crossover fanfictions. She has to learn to trust and work with new characters from different universes. And adaptation is very common too. She has to adapt to new environments, rules, and challenges in the crossovers.
It could also be that Katara was being overly critical of Aang's progress in learning new skills. Aang might feel frustrated and angry if Katara is constantly pointing out his flaws instead of being more encouraging, especially if he's already trying his best.
Their relationship would likely become more intimate and complex. They would have to rely on each other more, sharing a bond that goes beyond their previous friendship or alliance. Zuko would probably become more protective of Katara, and Katara would trust Zuko with her vulnerability during pregnancy.
Common themes might include their different worldviews colliding. Jet has his more radical ideas about fighting the Fire Nation, while Katara has her own moral compass. Their relationship development in the face of these differences could be a theme. Another could be the exploration of their individual backstories and how that affects their connection.
Another theme is the power of forgiveness. Katara has to forgive Zuko for things he has done in the past. Fanfictions often explore how this forgiveness is a key step in their relationship. For example, in many stories, Katara's ability to see the new Zuko and forgive the old one is what allows their love to bloom.