We study humanoid navigation across multiple destinations under long-horizon language instructions. This task is challenging because robots must maintain progress across successive goals while continuously producing natural, stable whole-body motion through confined spaces. However, task decomposition in existing methods does not by itself ensure progress throughout execution, while waypoint-based navigation does not guarantee natural, route-faithful whole-body motion. Our key idea is to organize navigation into three complementary roles operating at different time scales: a Brain for task reasoning, a Cerebellum for local motion generation, and a Brainstem for whole-body execution. We realize this idea in LHNav, an asynchronous system that uses progress and arrival feedback to coordinate navigation goals, VLA motion-token prediction, and whole-body control. To train the Cerebellum for natural, route-faithful motion, we develop a physics-grounded data engine that improves physical tracking of motion references along collision-aware routes and pairs the resulting demonstrations with rendered visual observations. Together, these designs allow task planning to proceed alongside continuous movement and extend single-goal navigation to successive destinations with natural, route-faithful whole-body motion. In simulation, our navigation VLA outperforms OmniNav and DualVLN in single-goal success and motion smoothness, with fewer collisions and falls. Using a VLA trained only on single-goal demonstrations, LHNav achieves a 75.56% success rate on long-horizon navigation tasks. Deployment on the Unitree G1 further demonstrates single-goal navigation and zero-shot long-horizon task execution in real-world environments, including layouts with repositioned objects. Project website: https://robbyant-research.github.io/LHNav/.

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