Line-of-sight link blockages represent a key challenge for the reliability and latency of millimeter wave (mmWave) and terahertz (THz) communication networks. This paper proposes to leverage LiDAR sensory data to provide awareness about the communication environment and proactively predict dynamic link blockages before they happen. This allows the network to make proactive decisions for handoff/beam switching which enhances its reliability and latency. We formulate the LiDAR-aided blockage prediction problem and present the first real-world demonstration for LiDARaided blockage prediction in mmWave systems. In particular, we construct a large-scale real-world dataset, based on the DeepSense 6G structure, that comprises co-existing LiDAR and mmWave communication measurements in outdoor vehicular scenarios. Then, we develop an efficient LiDAR data denoising (static cluster removal) algorithm and a machine learning model that proactively predicts dynamic link blockages. Based on the real-world dataset, our LiDAR-aided approach is shown to achieve 95% accuracy in predicting blockages happening within 100ms and more than 80% prediction accuracy for blockages happening within one second. If used for proactive hand-off, the proposed solutions can potentially provide an order of magnitude saving in the network latency, which highlights a promising direction for addressing the blockage challenges in mmWave/sub-THz networks.