The establishment of lunar bases introduces unprecedented challenges in energy management, where precise DC power forecasting is pivotal for ensuring uninterrupted power supply and efficient resource utilization in microgrids. With primary reliance on solar energy, supplemented by battery systems, forecasting energy availability becomes critical due to the Moon's unique conditions, such as prolonged night cycles, temperature extremes, and unpredictable dust storms. Conventional forecasting methods fall short in addressing these challenges, paving the way for advanced artificial intelligence (AI) techniques. This paper reviews state-of-the-art AI-driven methods, including machine learning (ML), deep learning (DL), hybrid models, and ensemble approaches. By synthesizing insights from existing literature and highlighting innovative applications, this review provides a comprehensive analysis of AI's transformative role in lunar power systems. Emphasis is placed on hybrid and optimization-based methods, supported by detailed flowcharts illustrating workflows. The paper identifies key research gaps and proposes future directions, including lightweight AI models for computational efficiency, digital twin integration for real-time optimization, and quantum computing for advanced forecasting. Additionally, it explores the integration of AI with other lunar base systems such as thermal regulation and life support, underscoring the interdisciplinary nature of sustainable extraterrestrial operations. The findings underscore AI's potential to revolutionize energy management in lunar microgrids, ensuring sustainable extraterrestrial operations.