As humanity looks toward the Moon for future exploration and potential habitation, energy management becomes one of the most critical challenges to ensure the success of long-term lunar missions. Lunar microgrids, designed to power lunar habitats and scientific equipment, must operate autonomously due to the extreme remoteness and harsh environmental conditions on the Moon. The integration of autonomous energy management systems (AEMS) can significantly improve the efficiency, resilience, and sustainability of lunar microgrids. This paper explores the essential role of autonomous energy management in lunar microgrids, emphasizing the challenges of lunar power generation, energy storage, and distribution. The unique environmental conditions on the Moon, including extended lunar nights, temperature extremes, radiation, and dust, demand a high level of system autonomy to guarantee continuous power supply without human intervention. Autonomous systems can automate power balancing, optimize energy use, and ensure the smooth operation of microgrids even during emergencies or failures. This paper also discusses current terrestrial applications of autonomous energy management, their adaptation for lunar use, and the integration of advanced technologies such as artificial intelligence (AI), machine learning, and predictive algorithms. Finally, the paper presents case studies and simulations illustrating the potential benefits of autonomous energy management for lunar microgrids and highlights areas for further research and development.