I installed the game through Steam and with Proton 5.0-7 as my default Steam Play choice. Run the game once to let it create all the files and folders it needs. You'll end up with a black windowed screen with just music playing in the background.

I exited both the game and Steam and run Lutris. Add new game, name it whatever you want then go to Configure. Under the Game Options tab and on the line for Executable, navigate to your Steam folders and choose the Game.exe from the Lust Epidemic folder. That will normally be in the path /Steam/steamapps/common/Lust Epidemic/Game.exe. Leave the Prefix architecture to Auto (default) and go to Runner options tab.

In Wine version, choose tkg-4.5-x86_64 (default) and make sure all the following switches under that are set to Off. Lastly on System options tab, Disable Lutris Runtime switch should be set to On. All other switches set to Off. Click save

Now with your new game configuration still highlighted, scroll down the right hand side and click Wine Configuration. Choose Windows XP on the Windows Version, then click Apply then OK

Now you can click on the Play button in Lutris to launch the game. It runs butter smooth for me after doing this :)