Efficient link configuration in millimeter wave (mmWave) communication systems is a crucial yet challenging task due to the overhead imposed by beam selection. For vehicle-to-infrastructure (V2I) networks, side information from LIDAR sensors mounted on the vehicles has been leveraged to reduce the beam search overhead. In this letter, we propose a federated LIDAR aided beam selection method for V2I mmWave communication systems. In the proposed scheme, connected vehicles collaborate to train a shared neural network (NN) on their locally available LIDAR data during normal operation of the system. We also propose a reduced-complexity convolutional NN (CNN) classifier architecture and LIDAR preprocessing, which significantly outperforms previous works in terms of both the performance and the complexity.