The Lunar Electromagnetic Monitor in X-rays (LEM-X) is a proposed lunar observatory for the study of highenergy transients. The fundamental components of the LEM-X instrument are pairs of coded aperture cameras, each sensitive in the 2 − 50 keV range and with a 2 sr field of view. In this paper, we present a trade-off analysis of the instrument layout, identify the optimal design, and characterize its performance in terms of sky exposure for multiple candidate landing sites. We first optimized the number and configuration of cameras and designed a concept of their support structure, to ensure complete and uniform sky coverage while minimizing complexity and volume. Then, by using NASA's SPICE toolkit, simulations were carried out to assess the effective sky coverage of the proposed instrument configuration. We provide results for three landing site candidates on the Moon's prime meridian, with latitudes 0 • , −70 • and −90 • , laying the groundwork for future mission implementation studies.