In the rapidly evolving landscape of autonomous mobile robots, the emphasis on seamless human-robot interactions has shifted towards autonomous decision-making. This paper delves into the intricate challenges associated with robotic autonomy, focusing on navigation in dynamic environments shared with humans. It introduces an embedded real-time tracking pipeline, integrated into a navigation planning framework for effective person tracking and avoidance, adapting a state-of-the-art 2D LiDAR-based human detection network and an efficient multi-object tracker. By addressing the key components of detection, tracking, and planning separately, the proposed approach highlights the modularity and transferability of each component to other applications. Our tracking approach is validated on a quadruped robot equipped with 270{\deg} 2D-LiDAR against motion capture system data, with the preferred configuration achieving an average MOTA of 85.45% in three newly recorded datasets, while reliably running in real-time at 20 Hz on the NVIDIA Jetson Xavier NX embedded GPU-accelerated platform. Furthermore, the integrated tracking and avoidance system is evaluated in real-world navigation experiments, demonstrating how accurate person tracking benefits the planner in optimizing the generated trajectories, enhancing its collision avoidance capabilities. This paper contributes to safer human-robot cohabitation, blending recent advances in human detection with responsive planning to navigate shared spaces effectively and securely.