Regression-based LiDAR relocalization has recently emerged as a promising solution for high-precision positioning in GNSS-denied environments. However, these methods are primarily tailored to autonomous driving, exhibiting significantly degraded accuracy in unmanned aerial vehicle (UAV) scenarios due to arbitrary pose variations and irregular flight paths. In this paper, we propose SOAR, a regression-based LiDAR relocalization framework for UAVs. Specifically, we introduce a locality-preserving sliding window attention module with locally invariant positional encoding to capture discriminative geometric structures robust to viewpoint changes. A coordinate-independent feature initialization module is further designed to eliminate sensitivity to global transformations. Furthermore, most existing UAV datasets are limited to evaluate LiDAR relocalization in real-world, due to the lack of synchronized LiDAR scans, accurate 6-DoF poses, or multiple traversals. Thus, we construct a large-scale UAV LiDAR localization dataset with 4 scenes and 13 irregular paths exhibiting rotation and altitude variations, providing a more realistic benchmark for UAVs. Extensive experiments demonstrate that our method achieves state-of-the-art performance, improving the localization success rate by 40% and reducing mean error over 10m on UAVLoc. Our code and dataset will be released soon.