Monitoring of vibrational eigenmodes of an elastic body excited by gravitational waves was one of the first concepts proposed for the detection of gravitational waves. At laboratory scale, these experiments became known as resonant bar detectors first developed by Joseph Weber in the 1960s. Due to the dimensions of these bars, the targeted signal frequencies were in the kHz range. Weber also pointed out that monitoring of vibrations of Earth or the Moon could reveal gravitational waves in the mHz band. His Lunar Surface Gravimeter experiment deployed on the Moon by the Apollo 17 crew had a technical failure, which greatly reduced the science scope of the experiment. In this article, we revisit the idea and propose a Lunar Gravitational-Wave Antenna (LGWA). We find that LGWA could become an important partner observatory for joint observations with the space-borne, laser-interferometric detector LISA and at the same time contribute an independent science case due to LGWA's unique features. Technical challenges need to be overcome for the deployment of the experiment, and development of inertial vibration sensor technology lays out a future path for this exciting detector concept.