Back when I was unable to get the launcher to run in Windows, I tried it in Linux just to see if it would go better. There was no difference.
After the HC Launcher was improved so I could run it in Windows, I ignored Linux until just now.
Ubuntu 20.04.1 LTS
Wine 5.0.12
Lutris 0.5.7.1
The Homecoming Launcher installed and ran with no issues. I have 64 bit City of Heroes running right now without any crashes.
Not relevant to this thread: I'm getting worse FPS than I do in Windows - I think I failed to install the proprietary driver for my nVidia GeForce GT 730.