The rapid expansion of artificial intelligence (AI) is driving an unprecedented increase in global computational demand, placing significant pressure on energy systems, water resources, and digital infrastructure. Current approaches focused on improving terrestrial efficiency are insufficient to address the long-term scalability limits of Earth-based data centers. This work proposes a latency-aware hybrid computing architecture that distributes AI workloads between Earth-based and lunar-based infrastructure according to their latency sensitivity. Real-time, latency-critical applications remain on Earth, while computationally intensive and latency-tolerant workloads—such as large-scale AI training, scientific simulations, and batch processing—are offloaded to lunar data centers powered by space-based solar energy. A quantitative framework is presented to evaluate key constraints, including energy consumption, thermal dissipation in vacuum environments, communication latency, and launch cost dynamics. The analysis incorporates energy modeling, infrastructure sizing, and economic break-even scenarios to assess feasibility under different technological conditions. Results indicate that while lunar data centers are currently constrained by high deployment and maintenance costs, they become increasingly viable under scenarios of reduced launch costs and sustained growth in AI energy demand. The proposed architecture introduces a new paradigm for planetary-scale computing, where workload segmentation based on latency constraints enables a more sustainable distribution of computational resources. This work contributes a novel perspective at the intersection of distributed systems, computational sustainability, and space-based infrastructure, providing a structured foundation for future research on off-Earth computing architectures.