Visual inspection of space-borne assets is of increasing interest to spacecraft operators looking to plan maintenance, characterise damage, and extend the life of high-value satellites in orbit. The environment of Low Earth Orbit (LEO) presents unique challenges when planning inspection operations that maximise visibility, information, and data quality. Specular reflection of sunlight from spacecraft bodies, self-shadowing, and dynamic lighting in LEO significantly impact the quality of data captured throughout an orbit. This is exacerbated by the relative motion between spacecraft, which introduces variable imaging distances and attitudes during inspection. Planning inspection trajectories with the aide of simulation is a common approach. However, the ability to design and optimise an inspection trajectory specifically to improve the resulting image quality in proximity operations remains largely unexplored. In this work, we present $\partial$LITE, an end-to-end differentiable simulation pipeline for on-orbit inspection operations. We leverage state-of-the-art differentiable rendering tools and a custom orbit propagator to enable end-to-end optimisation of orbital parameters based on visual sensor data. $\partial$LITE enables us to automatically design non-obvious trajectories, vastly improving the quality and usefulness of attained data. To our knowledge, our differentiable inspection-planning pipeline is the first of its kind and provides new insights into modern computational approaches to spacecraft mission planning. Project page: https://appearance-aware.github.io/dlite/