I use Ubuntu 22.04 and I'm able to run Leadwerks 4.6 with Proton version 7.0-6 (newer versions didn't work), and it works great.
Except for two things:
Script Editor: No autocomplete. I use VSCodium with the Leadwerks Add-on (can be found on the VS Code marketplace).
Running the game from the editor (both normal and debug modes) works only once, the second time, it will crash the whole editor. Instead, I run it from the terminal with Wine (wine "ProjectName".exe). If you want to run the game natively on Linux, publish the game as standalone first, then make the file "ProjectName" executable and run the game the same as any sh script. If you run the game as an sh script from the developing folder, you may experience texture and collider issues.