Here is what I have learned since installing my lift this fall:
You probably have bump-steer induced death wobble
Your front steering is going nuts because the stabilization is poor. Did you piece together a kit with control arms from different suppliers?
The death wobble you're experiencing is from the steering being at too low an angle. (from the side, your axle is rotated too far forward, by having long uppers or too short lowers). Tell us your upper and lowers length, and the mounting used (drop brackets?). A steering stablizer won't really help if your steering knuckles are close to straight up and down, because the momentum of your jeep is a destabilizing force greater than a little shock at higher speeds if the caster is destabilizing.
-When I first put in my lift, I was close to 0 degrees, and so I had the kind of shake you're talking about. First time it happened it took me by surprise.
The bump steer is caused by the trackbar and steering thingy (drag link) from not being parallel and not being of the same length. When the suspension cycles, the two take different arcs, and so the wheels turn. Fix what you can, and realize that every time your front end hits a good bump, the steering changes. Either the wheel in your hands will move left and right, or your front wheels will. To see how bad the bump steer is, just jump up and down on your front bumper (or to that effect), and watch the steering wheel rotate. If you were driving and hit the same bump, and were to grip the steering wheel tightly, the wheels would turn commensurate to how much you saw the steering wheel turn.
A lift supplier recommended that I tell the alignment shop to set the toe in at the max factory spec, but its a crutch so you should check out this other stuff first.
I'd only recommend a new steering stabilizer if your problem was small and that there was no other way to fix it cheaply. If the shake is like driving over railroad ties with no suspension, then you need to change some geometry to get stability back.
EDIT: yes, tell us your suspension situation, since this is modified tech