The Lunar-Earth Gravitational Assist (LEGA) of 19–20 August 2024 marked the first in-flight opportunity beyond functional checks to perform MAJIS (Moons and Jupiter Imaging Spectrometer) observations on-board the ESA's Jupiter Icy Moons Explorer (JUICE) spacecraft. This unique double flyby involved sequential close approaches to the Moon and Earth, offering an unprecedented configuration to evaluate MAJIS under high radiance, rapidly changing geometric, and operationally constrained conditions. A total of 24 hyperspectral image cubes were acquired (5 targeting the Moon and 19 the Earth) providing a dataset of approximately 7.5 Gbit. This work presents the primary goal of this observation campaign, which was to verify key aspects of MAJIS performance, including radiometric and spectral calibration, straylight behavior, geometric alignment, the use of onboard browse products, and interference tests with other JUICE instruments. This event also enabled assessment of thermal behavior and susceptibility to electromagnetic interference, and provided a first operational benchmark for MAJIS and a basis for refining future observation strategies and data analyses during JUICE's cruise and science phases. In addition, despite limited spatial and temporal coverage of the observations, the analyses presented here and in a series of companion papers of the special issue "<em>The first-ever lunar-Earth flyby: a unique test environment for JUICE</em>" demonstrated the instrument's ability to characterize mineralogical features on the Moon and atmospheric constituents on Earth. Observations include detection of mafic minerals (some associated to fresh excavated materials), thermal emission, and emissivity variations on the Moon at spatial scale of 100–200 m. Characterization of atmospheric absorption features, thermal brightness, icy cloud properties are captured for the Earth at km-scale and shortly discussed in the framework of the atmospheric biosignatures relevant to exoplanet habitability studies. Near-coincident acquisitions with other JUICE instruments and Earth-orbiting spectrometers provided valuable inter-calibration and cross-validation opportunities.