Another possibility is a crossover with Re:Zero. The time - looping concept of Re:Zero could be introduced into Log Horizon. Characters from Log Horizon might have to deal with constantly resetting situations and use their wits to break out of the loops and continue their journey in their own world.
First, you need to be familiar with both the Log Horizon universe and the other universe you want to cross it with. Read up on their characters, settings, and rules. For example, if it's a crossover with Naruto, understand how chakra works in Naruto and how the game mechanics work in Log Horizon.
One great fanfiction could be about Shiroe and Akatsuki exploring a new and dangerous area in the world of Log Horizon. They might face unique monsters and puzzles together, strengthening their bond along the way.
One idea could be that the characters from Sword Art Online find themselves in the world of Log Horizon. They could be confused by the different rules of the game world in Log Horizon, especially the unique economic and social systems. For example, Shiroe's knowledge of the game mechanics could either be a great help or a source of conflict when dealing with the SAO characters who are used to a more combat - centered gameplay.
Kirito from SAO might initially be a bit skeptical of the more complex systems in Log Horizon. He's used to a more straightforward 'fight and level up' kind of world. But he could gradually come to respect Shiroe's intelligence and leadership in understanding the game world on a deeper level. Asuna, on the other hand, could bond with some of the female characters in Log Horizon over the shared experience of being in a virtual world and having to deal with various challenges.
One unique feature is the combination of different power systems. Naruto has chakra - based powers, while Log Horizon has a more game - like power structure. In fanfictions, seeing how these two interact is really interesting.
The 'log horizon novel' is a story set in a virtual game world where players find themselves unable to log out. It's filled with elements of fantasy and adventure. The characters in the novel come from different backgrounds and have different skills. They must use their wits and cooperation to create a stable life in this new, unexpected environment. There are battles against monsters, negotiations with other player - run communities, and the constant exploration of the secrets of the virtual world. It shows how these players transform from ordinary gamers to survivors and leaders in this strange new world.