We present a combined strong and weak gravitational-lensing analysis of the massive galaxy cluster MACS J1423.8+2404 (z = 0.545, MACS J1423 hereafter), one of the most dynamically relaxed and massive cool-core clusters discovered in the MAssive Cluster Survey at z > 0.5. We combine high-resolution imaging from the Hubble Space Telescope (HST) in the F606W, F814W, and F160W pass-bands with spectroscopic observations taken as part of the KALEIDOSCOPE survey with the Multi-Unit Spectroscopic Explorer mounted on the Very Large Telescope. Our strong lensing analysis of the mass distribution in the cluster core is constrained by four multiple-image systems (17 individual images) within redshift range 1.779 < z < 2.840. Our weak lensing analysis of the cluster outskirts, confined to the HST field of view, is based on a background galaxy catalogue with a density of 57 gal arcmin−2. We measure a projected mass of M(R < 200 kpc) = (1.6 ± 0.05) × 1014 M☉ from our strong lensing model, and a projected mass of M(R < 640 kpc) = (6.6 ± 0.6) × 1014 M☉ when combining with our the weak lensing constraints. Our analysis of the cluster mass distribution yields no evidence of substructures, confirming the dynamically relaxed state of MACS J1423. Our work sets the stage for future analysis of MACS J1423 in the upcoming Canadian Near-Infrared Imager and Stiltless Spectrograph Unbiased Cluster Survey for the JWST.