Nope. I have no experience with Lutris, mainly because I'm tend to keep games natively. This guide is an exception because someone needs help in another thread.
I tried these steps recently and they do not work sadly on the currently build of Zorin Core. I even tried the updated binary files from Eve Online main page, but it just didn't work. I also went the Lutris route, and that did not work either. I'd be curious to see if we can get this to work and install originally like this.
What I can say and would like to contribute what worked to get Eve Online working running on Zorin 16:
Downloaded Steam through software store
In Settings under Steam Play checkmark Enable Steam Play for all other titles
Then either here select, or in the settings under Eve Online after you install it, make sure you use Proton 5.0-10
This was the only way I could get Eve Online to work properly under Zorin OS 16 with only this specific proton enabled. Usually any other Proton selected in the settings the game would crash right when you would enter your login credentials.
Just figured I'd put a little update after spending many hours trying to troubleshoot why it wouldn't work as easy as it should unfortunately.