We present a novel method for the autonomous positioning of surgical lamps in open surgeries. The basic idea is to use an inexpensive depth camera to track all objects and the surgical staff and also generate a dynamic online model of the operation situs. Based on this information, our algorithms continuously compute the optimal positions for all surgical lamps. These positions can then be communicated to robotic arms so that the lamps mounted on their end effectors will move autonomously. This will ensure optimal lighting of the operation situs at all times, while avoiding occlusions and shadows from obstacles. We tested our algorithm in a VR simulation using real-world depth camera data that was recorded during a real abdominal operation. Our results show that our method is robust and can ensure close-to-optimal lighting conditions in real-world surgeries with an update rate of 20 Hz.