Can we get a linux exe?

This will not answer your question, but the server.exe is just that, a very simple, already complied executable file that you can run win wine, no problem at all. Given that it's a node server, I'd suggest double-checking that you're not missing any dependencies, but it's most likely to start just fine the very first time you run it.

You can do in any way that works best for you, too, be it running it directly via your own terminal like

$ wine path/to/Aki.Server.exe

or create a Lutris entry. In case you want the latter, though, when configuring the exe, navigate to System settings and turn on the option to run in a command line mode (I don't remember the exact wording, sorry). Both work with identical results for me, so I guess your ubuntu server should be fine as well.

Hit me up if you have any other questions, I just got the whole thing to run on my Linux drive this weekend, so maybe I could help you out in case of trouble.