Mine did same thing - 2006 LR3. Irritating whining/whirling noise, showed up out of blue, did not go away. At first I thought it was AC or Power Steering pump pulley bearing on Serpentine belt or belt itself. I watched some youtubes for idea's and bought a mechanics stethoscope. I was into it by then and couldn't wait. Found a long piece of heavy wire, cut bottom off a milk gallon jug and bent wire to fit in milk lid hole. (red-neck stethoscope), no need to get head close to rotating belt, the videos of guys using screw drivers to listen, kind of worried me.
Any way, the good news was I found the source of the noise was the back belt's tensioner pulley bearings. The bad news was I still needed to get the fan clutch off the water pump housing in order to get access. Had to remove some covers; Engine cover, Fan Cowl and Air flow cover and tube.
The fan nut mounted to water pump required a couple new wrenches, a 36mm breaker bar wrench from Atlantic British worked, I bought several others that jaws got spread and didn't budge the nut. Also a universal water pump wrench, also a long breaker bar. It was a major chore to crack/loosen/remove that nut. Positioned the fan nut position, held nut with water pump wrench, with a pipe slid on handle for extra leverage. Had girlfriend hold that from passenger side. I got on driver side with 36mm and breaker bar. Some straining, a few slips, and great satisfaction when it broke loose. Removed the nut and fan and had some room to maneuver.
In my case, after that it was much easier. Hate to even think about if it had been bearing on some other accessory. So, anyways I took tension off belt and unseated the belt from several pulleys on driver side, to get it off the tensioner. Then removed the tensioner pulley, which is only one bolt, but after removing bolt, housing was gunked up and stuck so I had to pry it off. Tension spring was fine, so I bought only the new bearing wheel, just the bearings were making the noise. Removed old wheel (bolt on back) with new part, restrung the belt, replaced fan, and fired it up to test (scary part), only to have car not start... Turns out that cover/ input of air to carb, has a sensor that wouldn't allow car to be started with it off. Replaced that, went to start truck again, and noise gone!
