Lighting systems based on light-emitting diodes (LEDs) possess many benefits over their incandescent counterparts including longer lifespans, lower energy costs, better quality of light and no toxic elements, all without sacrificing consumer satisfaction. Their lifespan is not affected by switching frequency allowing for better illumination control and system efficiency. In this paper, we present a fully distributed energy-saving illumination dimming control strategy for the system of a lighting network which consists of a group of LEDs and user-associated devices. In order to solve the optimization problem, we are using a distributed approach that utilizes factor graphs and the belief propagation algorithm. Using probabilistic graphical models to represent and solve the system model provides for a natural description of the problem structure, where user devices and LED controllers exchange data via line-of-sight communication.