International audienceWe present a statistical analysis of a sample of 20 strong lensing clusters drawn from the Local Cluster Substructure Survey, based on high-resolution Hubble Space Telescope imaging of the cluster cores and follow-up spectroscopic observations using the Keck-I telescope. We use detailed parametrized models of the mass distribution in the cluster cores, to measure the total cluster mass and fraction of that mass associated with substructures within R <= 250kpc. These measurements are compared with the distribution of baryons in the cores, as traced by the old stellar populations and the X-ray emitting intracluster medium. Our main results include: (i) the distribution of Einstein radii is lognormal, with a peak and 1σ w...