Non-terrestrial network (NTN)-based integrated communication and computation empowers various emerging applications with global coverage. Yet this vision is severely challenged by the energy issue given the limited energy supply of NTN nodes and the energy-consuming nature of communication and computation. In this paper, we investigate the energy-efficient integrated communication and computation for the ground node data through a NTN, incorporating an unmanned aerial vehicle (UAV) and a satellite. We jointly consider ground data offloading to the UAV, edge processing on the UAV, and the forwarding of results from UAV to satellite, where we particularly address the uncertainties of the UAV-satellite links due to the large distance and high dynamics therein. Accordingly, we propose to minimize the weighted energy consumption due to data offloading, UAV computation, UAV transmission, and UAV propulsion, in the presence of angular uncertainties under Gaussian distribution within the UAV-satellite channels. The formulated problem with probabilistic constraints due to uncertainties is converted into a deterministic form by exploiting the Bernstein-type inequality, which is then solved using a block coordinate descent framework with algorithm design. Simulation results are provided to demonstrate the performance superiority of our proposal in terms of energy sustainability, along with the robustness against uncertain non-terrestrial environments.