Non-repetitive solid-state LiDAR scanning leads to an extremely sparse measurement regime for detecting airborne UAVs: a small quadrotor at 10-25 m typically produces only 1-2 returns per scan, which is far below the point densities assumed by most existing detection approaches and inadequate for robust multi-target data association. We introduce an unsupervised, LiDAR-only pipeline that addresses both detection and tracking without the need for labeled training data. The detector integrates range-adaptive DBSCAN clustering with a three-stage temporal consistency check and is benchmarked on real-world air-to-air flight data under eight different parameter configurations. The best setup attains 0.891 precision, 0.804 recall, and 0.63 m RMSE, and a systematic minPts sweep verifies that most scans contain at most 1-2 target points, directly quantifying the sparsity regime. For multi-target tracking, we compare deterministic Hungarian assignment with joint probabilistic data association (JPDA), each coupled with Interacting Multiple Model filtering, in four simulated scenarios with increasing levels of ambiguity. JPDA cuts identity switches by 64% with negligible impact on MOTA, demonstrating that probabilistic association is advantageous when UAV trajectories approach one another closely. A two-environment evaluation strategy, combining real-world detection with RTK-GPS ground truth and simulation-based tracking with identity-annotated ground truth, overcomes the limitations of GNSS-only evaluation at inter-UAV distances below 2 m.