Unfortunately, no. You'll need to get yourself a Blu Ray Player or a Playstation 3. OR - just download LOTR as a standard movie file, put it on a USB stick or portable hard drive, and plug THAT into your XBOX 360
The xbox 360 can play normal DVDs but not Blu-ray discs. You need a playstation 3 or a blu-ray player.
The original Xbox COULD play DVDs but, you needed the Xbox Media remote which came with a sensor which plugged into the controller port for it to play.