  We study the relation between the internal structure of early-type galaxies
and their environment using 70 strong gravitational lenses from the Sloan ACS
Lens Survey. The Sloan database is used to determine two measures of
overdensity of galaxies around each lens: the projected number density of
galaxies inside the tenth nearest neighbor (\Sigma_{10}) and within a cone of
radius one h^{-1} Mpc (D_1). Our main results are: 1) The average overdensity
is somewhat larger than unity, consistent with lenses preferring overdense
environments as expected for massive early-type galaxies (12/70 lenses are in
known groups/clusters). 2) The distribution of overdensities is
indistinguishable from that of "twin" non-lens galaxies selected from SDSS to
have the same redshift and stellar velocity dispersion \sigma_*. Thus, within
our errors, lens galaxies are an unbiased population, and the SLACS results can
be generalized to the overall population of early-type galaxies. 3) Typical
contributions from external mass distribution are no more than a few per cent,
reaching 10-20% (~0.05-0.10 external convergence) only in the most extreme
overdensities. 4) No significant correlation between overdensity and slope of
the mass density profile of the lens is found. 5) Satellite galaxies (those
with a more luminous companion) have marginally steeper mass density profiles
than central galaxies (those without). This result suggests that tidal
stripping may affect the mass structure of early-type galaxies down to kpc
scales probed by strong lensing, when they fall into larger structures
[ABRIDGED].
