As lunar exploration missions grow increasingly complex, ensuring safe and autonomous rover-based surface exploration has become one of the key challenges in lunar exploration tasks. In this work, we have developed a lunar surface simulation system called the Lunar Exploration Simulator System (LESS) and the LunarSeg dataset, which provides RGB-D data for lunar obstacle segmentation that includes both positive and negative obstacles. Additionally, we propose a novel two-stage segmentation network called LuSeg. Through contrastive learning, it enforces semantic consistency between the RGB encoder from Stage I and the depth encoder from Stage II. Experimental results on our proposed LunarSeg dataset and additional public real-world NPO road obstacle dataset demonstrate that LuSeg achieves state-of-the-art segmentation performance for both positive and negative obstacles while maintaining a high inference speed of approximately 57\,Hz. We have released the implementation of our LESS system, LunarSeg dataset, and the code of LuSeg at:https://github.com/nubot-nudt/LuSeg.