I can use for example EGS on Lutris with no problem so I think issue is on your end.
Can you give system specs following this thread? [HowTo] Provide System Information
Did you customize anything in Lutris?
Did you follow the instruction on Lutris site?
Gold: works flawlessly with some minor tweaking
CONFIGURE AND INSTALL THE DEPENDENCIES FIRST
Instructions for Vulkan support: Installing drivers · lutris/lutris Wiki · GitHub
Instructions for proper functionality of Battle.Net (+ common problems) Game: Blizzard App · lutris/lutris Wiki · GitHub
IMPORTANT NOTES
- The installer provides a pre-generated DXVK state cache to provide stutter-free experience. As a result, it will cause a temporary performance hit while the shaders are being compiled. The FPS will rise back up after it has finished.