Can you run either a windowed or true full screen visualizer on a second display while not taking over the first display as well?
yes lion will put full screen apps (like itunes visualizer) in mission control so all you have to do in swipe to the left with two fingers and there is your itunes and desk top then swipe back to the right and there is your visualizer. of course first you have to launch visualizer... mission control also allows you to use multiple desk tops a one time. you should try to find the video apple has on lion. if they no longer have it on there site (because they have the mountain lion video on there now, coming out this summer), then I would check to see if it is on you tube.