The Lunar Gravitational-Wave Antenna is a proposed low-frequency gravitational-wave detector on the Moon surface. It will be composed of an array of high-end cryogenic superconducting inertial sensors (CSISs). A cryogenic environment will be used in combination with superconducting materials to open up pathways to low-loss actuators and sensor mechanics. CSIS revolutionizes the (cryogenic) inertial sensor field with a modelled displacement sensitivity at 0.5 Hz of 3 orders of magnitude better than the current state-of-the-art. It will allow the Lunar Gravitational-Wave Antenna to be sensitive below 1 Hz, down to 1 mHz and it will also be employed in the forthcoming Einstein Telescope-a third-generation gravitational-wave detector which will make use of cryogenic technologies and that will have an enhanced sensitivity below 10 Hz. Moreover, CSIS seismic data could also be employed to obtain new insights about the Moon interior and what we can call the Selene-physics.