In this paper, we consider the transformation of laser range measurements into a top-view grid map representation to approach the task of LiDAR-only semantic segmentation. Since the recent publication of the SemanticKITTI data set, researchers are now able to study semantic segmentation of urban LiDAR sequences based on a reasonable amount of data. While other approaches propose to directly learn on the 3D point clouds, we are exploiting a grid map framework to extract relevant information and represent them by using multi-layer grid maps. This representation allows us to use well-studied deep learning architectures from the image domain to predict a dense semantic grid map using only the sparse input data of a single LiDAR scan. We compare single-layer and multi-layer approaches and demonstrate the benefit of a multi-layer grid map input. Since the grid map representation allows us to predict a dense, 360° semantic environment representation, we further develop a method to combine the semantic information from multiple scans and create dense ground truth grids. This method allows us to evaluate and compare the performance of our models not only based on grid cells with a detection, but on the full visible measurement range.