Constraints on the mass distribution in high-redshift clusters of galaxies are currently not very strong.\ud Aims. We aim to constrain the mass profile, M(r), and dynamical status of the z ∼ 0.8 LCDCS 0504 cluster of galaxies that is characterized\ud by prominent giant gravitational arcs near its center.\ud Methods. Our analysis is based on deep X-ray, optical, and infrared imaging as well as optical spectroscopy, collected with various\ud instruments, which we complemented with archival data. We modeled the mass distribution of the cluster with three different mass\ud density profiles, whose parameters were constrained by the strong lensing features of the inner cluster region, by the X-ray emission\ud from the intracluster medium, and by ...