Love and friendship are very common themes. Most fanfics focus on how Korra and Asami's relationship grows from being friends to something more. They often show how they support and understand each other.
A common theme is friendship evolving into love. Many fanfics start with their strong friendship, like in the show, and then show how that bond deepens into romantic feelings over time.
One common theme is their relationship development. It often explores how they first realize their feelings for each other. Another theme could be adventure. Writers might put them in new and exciting situations while also showing their relationship growing.
One possible fanfic could be about Asami getting jealous when Korra spends a lot of time with another character. Maybe Korra has to work closely with someone on a new project in Republic City, and Asami starts to feel left out. Asami might try to hide her jealousy at first, but it eventually bubbles to the surface during a dinner with Korra and the others.
One great 'korra x asami fanfic' is 'The New Beginnings'. It beautifully explores their relationship as they navigate the post - war world together. The character development is really well - done in this fic.
There's 'A New Bond'. In this fanfic, Asami and Korra face various challenges in Republic City. It focuses on how their friendship gradually turns into something more. It has really nice character development for both of them.
Fanfiction.net could also be a place to look for korra x asami lesbian fanfic. However, the tagging system might not be as detailed as AO3. You'll need to search carefully. Maybe start with searching for 'Korra' and 'Asami' and then look through the results to find the ones that match what you're looking for.
One common theme is the exploration of their different backgrounds. Korra is from the South Pole and Asami is from a more urban, technological background. Fanfictions often play with how these differences bring them together.