Yes, there are quite a few. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for 'lwa akko x andrew' and you'll find a variety of stories. Some might focus on their relationship development, while others could be more adventure - based with their relationship as a side plot.
One common theme is the 'opposites attract' idea. Akko is often seen as more impulsive and energetic, while Andrew is more reserved. Another theme could be about bridging the gap between different worlds, as they come from different backgrounds. For example, Akko from the magical world and Andrew from a more traditional non - magical one.
Akko might encounter a group of rebel witches. These witches have their own unique way of using magic, different from what she learned at Luna Nova. They might initially be suspicious of her but then become her friends and teach her their style of magic. They could also help her understand that there are many ways to be a witch, not just the way the school teaches.
There could be Lotte and Sucy. Lotte might be there to support Akko with her bookish knowledge of magic, while Sucy could add some comical and mischievous elements to the story.
I'm not entirely sure specifically what a particular 'akko dies fanfic' is about without reading it. It could be a fan - created story where the character Akko meets an unfortunate end. It might explore the reactions of other characters in the story's universe, or it could be a very dark and alternate take on the original story where Akko's death serves as a major plot device to explore themes like grief, sacrifice, or the consequences of certain actions.
A key element is the exploration of their relationship. Usually, it's about Akko's admiration for Chariot and how Chariot, in turn, becomes a mentor - like figure to Akko. For example, in many fanfics, Chariot helps Akko with her magic skills.
One common theme is inspiration. Akko is often inspired by Chariot's achievements in magic. For example, in many fics, Akko discovers something about Chariot's past glories and it gives her the motivation to overcome her own difficulties in learning magic at Luna Nova.
Love and friendship are very common themes. Many fanfics explore how Akko and Andrew's relationship evolves from just acquaintances to friends and sometimes more. Another theme is growth. They both grow as individuals and in their relationship.
One characteristic is the exploration of their contrasting personalities. Diana is often seen as refined and studious, while Akko is impulsive and full of energy. Fanfictions play with these differences to create interesting interactions. For instance, they might start off clashing but then gradually find common ground.