Low Earth Orbit (LEO) satellite constellations are poised to become a critical component of next-generation communication infrastructure, offering low-latency and high-bandwidth connectivity. However, their limited computational resources pose challenges for implementing advanced applications like Federated Learning (FL). To address this, we propose a cluster-based satellite edge micro-cloud computing architecture for FL in LEO constellations. This architecture organizes client satellites into micro-cloud clusters, each with dedicated server and client nodes, enabling efficient distributed computation. We propose a comprehensive mathematical model incorporating privacy budgets, security threat metrics, latency constraints, and energy consumption. To optimize FL performance within this architecture, we propose a Lyapunov-driven heuristic approach, decomposing the optimization problem into sub-problems for satellite selection and privacy noise adjustment. This approach dynamically selects optimal server satellites, adjusts privacy noise, and minimizes long-term average latency and energy consumption while adhering to constraints. We demonstrate the effectiveness of our approach through simulations, showcasing improved FL performance and resource utilization in LEO satellite clusters.