Why does it vibrate you ask?
Well, it's actually a complex subject. It involves lots of math and geometry of driveline angles, Cardan joints and rotational velocities. Who cares? Not me. Let's just describe the problem in simple terms.
The driveline and u-joints on your Disco must keep a constant turning velocity to transfer torque from the output of the transfer case flange to the input of the differential pinion flange. As long as those flanges are pointing at each other the driveline is straight and all works perfectly well. Of course, when you drive over bumps, the differential end will move up and down with the axel. The u-joints allow the driveline to flex around and follow the movement and still keep up that constant turning velocity. The u-joints can do this as long as the angles they turn at are equal. That is the magic of u-joints. The problem begins when the angles in the u-joints are not equal to each other. Then the drive shaft must wobble a little bit to keep the velocity constant. When you lift the Disco, the transfer case flange is lifted along with the truck. Since the differential is part of the full floating axel, its position does not change. So one end has moved up but the other end stayed put; the angles in the u-joints are no longer equal. The u-joints will still do their thing and provide a constant turning velocity, it's just that one end will have to wobble a bit to do it. When the Disco gets going, the little wobbles can add up to some big time vibration!
What can I do about it?
Generally, because of the driveline's shorter length, the front u-joint's angles are affected more and become the vibrating problem. Replacement drivelines are available that have a constant velocity joint built onto the transfer case end of the shaft. This solves the problem nicely since all the velocity changing is done in that CV joint. The CV is made from a pair of back-to-back u-joints, phased just right to cancel out any velocity changes due to extreme driveline angles. The shaft is free to turn at almost any angle without worries of wobble or vibration. The Disco is smooth once again!
Drive the Disco after the lift. The old driveline is going to work for now. If it vibrates, buy a CV driveline and change it! Otherwise, you are going to annoy friends and family and give Land Rovers everywhere a bad name. Face it, you don't want people to mistake that luxurious Disco for some old rattletrap Jeep. You will also wear out the u-joints in record time and that is not good either. If it drives smooth like before, your lift has not upset the driveline angles too much so you don't need to worry.
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NEW CV-JOINTED DRIVE SHAFT