This paper investigates energy efficiency maximization in an integrated sensing and communication framework for satellite-UAV MIMO systems, where a LEO satellite and a UAV simultaneously serve ground users and perform target sensing. Both the satellite and UAV are equipped with uniform planar arrays of transmit antennas, enabling a distributed multi-user and multi-target architecture. We derive the achievable downlink throughput by considering that the high-altitude satellite maintains a line-of-sight (LoS) link with users, while adopting a probabilistic model for the UAV that accounts for the likelihood of both LoS and non-line-of-sight conditions. The energy efficiency maximization problem is formulated as a complex non-convex optimization problem, subject to power constraints, quality of service (QoS) requirements, and beampattern gain constraints for accurate sensing. To tackle this challenge, we propose an efficient alternating optimization algorithm capable of handling the complex search space and QoS guarantees. Numerical results across diverse scenarios with multiple users demonstrate that the proposed method achieves high energy efficiency while meeting both communication and sensing performance targets.