  We present a statistical analysis of a sample of 20 strong lensing clusters
drawn from the Local Cluster Substructure Survey (LoCuSS), 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
parameterized 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 log-normal, with a peak and 1sigma width of
<log(RE(z=2))>=1.16+/-0.28; (ii) we detect an X-ray/lensing mass discrepancy of
<M_SL/M_X>=1.3 at 3 sigma significance -- clusters with larger substructure
fractions displaying greater mass discrepancies, and thus greater departures
from hydrostatic equilibrium; (iii) cluster substructure fraction is also
correlated with the slope of the gas density profile on small scales, implying
a connection between cluster-cluster mergers and gas cooling. Overall our
results are consistent with the view that cluster-cluster mergers play a
prominent role in shaping the properties of cluster cores, in particular
causing departures from hydrostatic equilibrium, and possibly disturbing cool
cores. Our results do not support recent claims that large Einstein radius
clusters present a challenge to the CDM paradigm.
