The ESA Lunar Lander mission is a step in the preparation for future exploration missions, being tasked with demonstrating autonomous soft, safe precision landing on the Moon. The last segment of the mission's descent and landing phase is the approach phase, during which the GNC subsystem steers the spacecraft to the targeted landing site (LS). The Hazard Detection and Avoidance (HDA) subsystem is active during this phase and uses the measurements provided by a camera and a LIDAR to assess the safety of the terrain. The HDA subsystem also determines which are the ground locations that can be reached by the spacecraft. Based on the safety and reachability assessments, the HDA subsystem then decides autonomously if a retargeting should be commanded to a new LS. In that case, the GNC subsystem is notified and tasked with driving the vehicle to perform a soft landing at the designated LS. This paper describes the concept and performances of the HDA subsystem proposed for the Lunar Lander mission. Sensitivity tests are performed in order to evaluate the robustness of the system. The performance of the HDA subsystem is demonstrated through Monte Carlo simulation campaigns on a functional engineering simulator.