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The light detection and ranging (LiDAR) technology allows to sense surrounding objects with fine-grained resolution in a large areas. Their data (aka point clouds), generated continuously at very high rates, can provide information to support automated functionality in cyberphysical systems. Clustering of point clouds is a key problem to extract this type of information. Methods for solving the problem in a continuous fashion can facilitate improved processing in e.g. fog architectures, allowing continuous, streaming processing of data close to the sources. We propose Lisco, a single-pass continuous Euclidean-distance-based clustering of LiDAR point clouds, that maximizes the granularity of the data processing pipeline. Besides its algorithmic analysis, we provide a thorough experimental evaluation and highlight its up to 3x improvements and its scalability benefits compared to the baseline, using both real-world datasets as well as synthetic ones to fully explore the worst-cases.