So I got Duke3D, unfortunately it is currently unplayable.
The game lags very badly, FPS ranging from 1-5 mostly. I've tried all the different graphic modes, as well as fiddling around with in-game settings to no avail.
It only starts lagging once the actual game starts up (first on the main menu, with the demo playing in the background). The intro animations before that roll smoothly.
It should be mentioned that I've installed the game on an external drive, and I'm playing through USB 2.0. But I've had no problems playing other games this way. I've even had Crysis installed on the external drive, playing that was no problem.
Also, after some time, anything from 1 to 10 minutes of trying to play with 2 average fps, DosBox hangs. The CPU cycles are at max. DosBox never eats more than ~10% CPU at any time.
Halp plx?

Yea, like ElPixelIlustre said, there is a good chance things work better with eDuke32

That did it, thanks.

Please explain "eDuke32". I purchased the Duke3D game from GOG. "Setup_duke3d.exe" is the only file provided. Am I supposed to find this "eDuke32" file somewhere else?

eDuke32 is a third party engine for the Duke Nukem 3D game. It's not the only one in existence either. Just do a Google search for it and you'll find it.
You will need to run the GOG installer first, though, in order for the game files to be extracted, because once you install eDuke32 (or any other engine for the game) you will need to copy some of the game files over into the eDuke32 program location.
As it is third party, GOG do not provide it with their installer. It also allows higher resolution, real 3D models, better mouselook, etc.