A new robust and accurate approach for the detection and localization of flying objects with the purpose of highly dynamic aerial interception and agile multi-robot interaction is presented in this paper. The approach is proposed for use on board of autonomous aerial vehicles equipped with a 3D LiDAR sensor. It relies on a novel 3D occupancy voxel mapping method for the target detection that provides high localization accuracy and robustness with respect to varying environments and appearance changes of the target. In combination with a proposed cluster-based multi-target tracker, sporadic false positives are suppressed, state estimation of the target is provided, and the detection latency is negligible. This makes the system suitable for tasks of agile multi-robot interaction, such as autonomous aerial interception or formation control where fast, precise, and robust relative localization of other robots is crucial. We evaluate the viability and performance of the system in simulated and real-world experiments which demonstrate that at a range of 20m, our system is capable of reliably detecting a micro-scale UAV with an almost 100% recall, 0.2m accuracy, and 20ms delay.