Noise depends on ISO and your camera, not the lens per se. The 5D-II is a good performer in that area.
The 135/2L is a great lens in every respect. Wide open, you can shoot in very dim conditions by ambient light. It's sharp, focuses quickly, and has very little distortion, CA or any other objectionable artifact even wide open. Except for the now-discontinued 200mm/1.8L, it's the sharpest lens Canon makes. The only drawback is that when shooting wide open, DOF is very narrow, as in fraction-of-an-inch narrow. In a typical headshot, if the subject isn't facing directly at the camera you won't be able to get both eyes in focus and if the eyes are in focus, the lips will be OOF. At longer distances, the DOF is more forgiving, but you'll always need to be very careful where you place focus.