This paper addresses the challenge of Lidar-Inertial Odometry (LIO) in dynamic environments, where conventional methods often fail due to their static-world assumptions. Traditional LIO algorithms perform poorly when dynamic objects dominate the scenes, particularly in geometrically sparse environments. Current approaches to dynamic LIO face a fundamental challenge: accurate localization requires a reliable identification of static features, yet distinguishing dynamic objects necessitates precise pose estimation. Our solution breaks this circular dependency by integrating dynamic awareness directly into the point cloud registration process. We introduce a novel dynamic-aware iterative closest point algorithm that leverages spatio-temporal normal analysis, complemented by an efficient spatial consistency verification method to enhance static map construction. Experimental evaluations demonstrate significant performance improvements over state-of-the-art LIO systems in challenging dynamic environments with limited geometric structure. The code and dataset are available at https://github.com/thisparticle/btsa.