dpkg -L [lutris_package_name]

This will show you where all the files for the install of Lutris are. You can find the name of the Lutris package with:

dpkg -l | grep lutris

If you're not seeing the binary to launch, just uninstall and reinstall the package.

Have you tried opening up the command line and typing in lutris?

Edit:

• Issue persists across system restarts
• Issue persists across uninstalling and reinstalling Lutris.

Try to look for a .desktop file in /usr/share/applications/

If it is not there, try making one in ~/.local/share/applications/

If there is no .desktop file, try looking for the binary with $ which lutris

If you find the binary, but can't find the .desktop file, take another .desktop file as an example from /usr/share/applications/ and create a new one in ~/.local/share/applications/ with appropriate Exec= from the $ which command from earlier

Lutris is a python application, you can do git clone on the GitHub repo and you car run lutris from there. This will also use your config files as they are stored in your home directory.

Have you considered using Heroic game launcher instead. I think its good as long as you use wine fixes instead of proton ones.

Edit: looks like lutris is installed but corrupted?

What about this command in terminal.

dpkg -l | grep -i lutris