Of all the conversions of Robotron: 2084 for the home, I like the Lynx version's firing controls best, despite it only having two buttons and a D-pad. Your gun fires continuously, as fast as possible, and you use the two buttons to rotate back and forth through the eight directions. Obviously not a perfect proxy for two joysticks, but close enough. (If I could figure out how to hook up a dual X-Arcade joystick to emulate two joysticks with something like Midway Arcade Treasures, that'd be ideal, but I don't see how to do that short of just building your own.)
The Lynx version runs noticeably slower than the original arcade game, and I'd like to know if this is intentional. With the smaller screen resolution, there is very little open space in which to work, so having the game run too quickly would actually make it nigh impossible. For example, check out the Robotron: 2084 screenshots over at AtariAge. So the added control precision permits this version to capture a good chunk of the claustrophobic panic of the original.
Finally, it is the one version of Robotron: 2084 that I know which has title screen music. It's aptly dark and it's my custom to listen to the whole thing any time I fire up Robotron: 2084 on the Lynx.
The answer you seek might be in here :
Try the different analog modes.
I also own an x-arcade stick, and i usually do robotron-esque things by changing the buttons in mame, but that is obviously when hooked up to a pc.
Also, when hooked up to a pc via ps2, you can rebind the keys however you want (http://www.x-arcade.com/service/images/Layouts/PC-MAC.htm)
I don't know about the usb mode, since I don't have the usb adapter (yet).
I love my x-arcade stick =)