I'm having issues running DK on Linux using Lubuntu 18 Bionic. I tried running with the included GoG DosBox config, then using stipped-down DoxBox commands with the same result. Instead of starting, the game simply quits. No graphics, no loading screen, just right back to the command prompt. The commands I tried were as follows:


Z:\MOUNT c ~/
Z:\IMGMOUNT d ~/DungeonKeeper/ -t iso -fs iso
Z:\C:
C:\cd Dungeo~1
C:DUNGEO~1\KEEPER.exe

And crash, right back to the C:\ prompt.

For installation on Ubuntu, I suggest you give a try to ./play.it.
It automates the installation process through the building of .deb packages, and use your system-provided version of DOSBox instead of the one shipped in the GOG installer.

I haven't tried play.it yet, but I don't see why it should matter. I'm already using the system DosBox instead of the GoG pre-packaged version.

By enforcing a standard way of installing and running the game, ./play.it provides a good way to debug such issues.
In your case it would help in understanding if there is an issue with your current DOSBox setup, or with the game files, or even with the commands you use to run the game.