The scene where Little Alex chases, and subsequently murders the Cat Lady is shot on a handheld 18mm Arriflex camera, and involves him moving around the room as the scene unfolds. The camera focuses on all four walls at some point throughout the shot, which means it would be impossible to set up lights in the room (you can see the ceiling too). Kubrick used his innovation, and actually included illuminated sculptures around the walls, which ended up lighting the room perfectly, and was soft enough to cast no shadows, including his own as he moved around the room.
This was not the first time Kubrick had used this technique; he used similar lighting in the war room in Dr. Strangelove and the circular space ship in 2001. I really like the whole aspect of him building the lighting into the scene as opposed to using set lighting. It adds a certain realistic and natural quality to the scene which in my opinion makes this shot rather eerie.