Scene parsing is a critical component for understanding complex scenes in applications such as autonomous driving. Semantic segmentation networks are typically reported for scene parsing but semantic edge networks have also become of interest because of the sparseness of the segmented maps. This work presents an end-to-end trained lightweight deep semantic edge detection architecture called LiteEdge suitable for edge deployment. By utilizing hierarchical supervision and a new weighted multi-label loss function to balance different edge classes during training, LiteEdge predicts with high accuracy category-wise binary edges. Our LiteEdge network with only ≈ 3M parameters, has a semantic edge prediction accuracy of 52.9% mean maximum F (MF) score on the Cityscapes dataset. This accuracy was evaluated on the network trained to produce a low resolution edge map. The network can be quantized to 6-bit weights and 8-bit activations and shows only a 2% drop in the mean MF score. This quantization leads to a memory footprint savings of 6X for an edge device.