I wouldn't put lock-tite on the nut underneath the clamp base. Tbuggle is right, tightening the nuts against each other is sufficient.
You need to open the clamp base on put something on the threads of the adjustment screw. Here's what's going on inside the clamp: When you turn the clamp's handle, a little plug pushes against the center of the base, locking clamp in place. The adjustment screw for the clamp base moves this plug closer or further from the center of the base, tightening or loosening the clamp base. The clamp bases come with some thread-lock goo on the threads of the adjustment screw. If you played around with the screw a bunch (like I did) by over-loosening and over-tightening the clamp, then you pushed most of the goo to the outer edges of the threads. As a result, each time you turn the handle, the adjustment screw is pushed a little further into the little plug, loosening the clamp base. I fixed this by opening up the clamp and pushing the goo back onto the threads of the adjustment screw. Alternatively, you could add some more goo to the threads, but I wouldn't use lock-tite. The object is to make the threads harder to turn but still adjustable. Lock-tite would lock them in place, but the benefit would be gone once you moved the screw and broke the seal.
The goo that comes with the clamps is sort of the consistency of grease but doesn't have the same lubricating properties. In fact, it does just the opposite, making the threads harder to turn. I can't remember what that stuff is called. Anyone out there know?
I don't think you want to use anything that will lock these threads. Instead, you just want something that sort of snugs them up. Make sense?