This is my experience getting Little Navmap working with my simulator running on Proton. I created this account specifically just to post this to help people who are migrating their sims to Linux.
My setup:
DISTRO: Arch Linux
DE/WM: Hyprland
SIM: MSFS2020 Steam running via Proton
Prerequisites:
Download the Linux .tar.gz version of LNM. Not the installer.
Download the Windows .zip version of LNM from the github repo. Not the installer.
Extract both separately in a convenient directory (we'll use ~/LittleNavmap/Linux and ~/LittleNavmap/Windows for this guide)
Install protontricks from your preferred package manager. (https://github.com/Matoking/protontricks)
Solution:
Launch your simulator
Execute this command in your terminal
protontricks -c "wine ~/LittleNavmap/Windows/Little Navconnect/littlenavconnect.exe" 1250410
Wait for the Little Navconnect window to show up
Launch the Linux version of LNM
Tools > Connect to Flight Simulator... > Hostname: 127.0.0.1
Wait for LNM to connect to LNC
Profit
Optionals:
(optional) Create a .desktop shortcut for the Linux executable of LNM (~/LittleNavmap/Linux/littlenavmap)
(optional) Create a .desktop shortcut for Little Navconnect using the protontricks command (~/LittleNavmap/Windows/Little Navconnect/littlenavconnect.exe)
Notes:
Running the Windows littlenavmap.exe directly via protontricks does work, but for me the UI is too laggy/sluggish maybe because of the additional Wine layer.
If your sim runs on Wine in a custom prefix, this solution should theoretically work with winetricks. Just make sure you set the pfx to your sim's wine prefix directory.
If you're still having trouble, reply here and describe your issue and I may be able to help you.