In this paper, we propose a three-dimensional movable lighting system consisting of multiple LED lighting units placed in a space. We aim to control the illuminance distribution in 3D space by appropriately determining the lighting arrangement and ON/OFF lighting pattern of the lighting system. In this paper, we first formulated the optimization problem of lighting arrangement and ON/OFF pattern. Then, we proposed an algorithm to solve the optimization problem, assuming that each LED lighting unit is placed in a box created by dividing the space into a grid. In order to solve the optimization problem, we introduce a virtual network model to communicate the excess and deficiency of illuminance. This approach can be applied to the constrained optimization problem with infeasible area in 3D space. The numerical calculation results are shown for a desired illuminance distribution with and without infeasible area on the lighting arrangement. Furthermore, we developed an experimental setup using 16 LED units. Finally, we verified the effectiveness of our algorithm by control experiments.