Spike sorting is a critical process for decoding large-scale neural activity from extracellular recordings. The advancement of neural probes facilitates the recording of a high number of neurons with an increase in channel counts, arising a higher data volume and challenging the current on-chip spike sorters. This paper introduces L-Sort, a novel on-chip spike sorting solution featuring median-of-median spike detection and localization-based clustering. By combining the median-of-median approximation and the proposed incremental median calculation scheme, our detection module achieves a reduction in memory consumption. Moreover, the localization-based clustering utilizes geometric features instead of morphological features, thus eliminating the memory-consuming buffer for containing the spike waveform during feature extraction. Evaluation using Neuropixels datasets demonstrates that L-Sort achieves competitive sorting accuracy with reduced hardware resource consumption. Implementations on FPGA and ASIC (180 nm technology) demonstrate significant improvements in area and power efficiency compared to state-of-the-art designs while maintaining comparable accuracy. If normalized to 22 nm technology, our design can achieve roughly $\times 10$ area and power efficiency with similar accuracy, compared with the state-of-the-art design evaluated with the same dataset. Therefore, L-Sort is a promising solution for real-time, high-channel-count neural processing in implantable devices.