Yeah, I install all of my Lutris games "manually". The process goes something like this:

1. Prerequisites
   • Download the MTGA installer
   • Create a directory where you want the MTGA wine prefix to live (I use /home/my_username/Games/mtg/)
2. In Lutris, press + to add a new game, and set the following:
   • Name: "Magic The Gathering Arena"
   • Runner: Wine
3. Click Game Options, set the following:
   • Executable: /path/to/MTGAInstaller.exe
   • Wine prefix: /path/to/your/wine/prefix/location/ (As I mentioned above, I use /home/my_username/Games/mtg/)
4. Click Save
5. Optional, if the game art doesn't auto-populate:
   • Click Lutris under "Sources" on the left -> Community Installers
   • Search for "magic arena", and wait for results to populate (the search downloads the art)
   • Exit the community installer section
6. Click Play in Lutris
   • From here it should set up the Wine prefix and install the game. Once that is done then quit the game (if it auto-launches).
7. Set Lutris to the game's launch executable: right-click on the MTGA icon -> Configure -> Game Options
   • Executable: /installed/path/to/MTGALauncher.exe (for me it is /home/my_username/Games/mtg/drive_c/Program Files/Wizards of the Coast/MTGA/MTGALauncher/MTGALauncher.exe)
8. Click Save and you should be good to go!

Good luck! If the game doesn't work following these instructions then you can try running with different versions of Wine (I'm using lutris-GE-Proton8-x86_64). And if it still doesn't work then I'd expect your issue might be with your GPU drivers.