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LiDAR semantic segmentation is crucial for autonomous vehicles and mobile robots, requiring high accuracy and real-time processing, especially on resource-constrained embedded systems. Previous state-of-the-art methods often face a trade-off between accuracy and speed. Point-based and sparse convolution-based methods are accurate but slow due to the complexity of neighbor searching and 3D convolutions. Projection-based methods are faster but lose critical geometric information during the 2D projection. Additionally, many recent methods rely on test-time augmentation (TTA) to improve performance, which further slows the inference. Moreover, the pre-processing phase across all methods increases execution time and is demanding on embedded platforms. Therefore, we introduce HARP-NeXt, a high-speed and accurate LiDAR semantic segmentation network. We first propose a novel pre-processing methodology that significantly reduces computational overhead. Then, we design the Conv-SE-NeXt feature extraction block to efficiently capture representations without deep layer stacking per network stage. We also employ a multi-scale range-point fusion backbone that leverages information at multiple abstraction levels to preserve essential geometric details, thereby enhancing accuracy. Experiments on the nuScenes and SemanticKITTI benchmarks show that HARP-NeXt achieves a superior speed-accuracy trade-off compared to all state-of-the-art methods, and, without relying on ensemble models or TTA, is comparable to the top-ranked PTv3, while running 24$\times$ faster. The code is available at https://github.com/SamirAbouHaidar/HARP-NeXt