  Using new photometric and spectroscopic data in the fields of nine strong
gravitational lenses that lie in galaxy groups, we analyze the effects of both
the local group environment and line-of-sight galaxies on the lens potential.
We use Monte Carlo simulations to derive the shear directly from measurements
of the complex lens environment, providing the first detailed independent check
of the shear obtained from lens modeling. We account for possible tidal
stripping of the group galaxies by varying the fraction of total mass
apportioned between the group dark matter halo and individual group galaxies.
The environment produces an average shear of gamma = 0.08 (ranging from 0.02 to
0.17), significant enough to affect quantities derived from lens observables.
However, the direction and magnitude of the shears do not match those obtained
from lens modeling in three of the six 4-image systems in our sample (B1422,
RXJ1131, and WFI2033). The source of this disagreement is not clear, implying
that the assumptions inherent in both the environment and lens model approaches
must be reconsidered. If only the local group environment of the lens is
included, the average shear is gamma = 0.05 (ranging from 0.01 to 0.14),
indicating that line-of-sight contributions to the lens potential are not
negligible. We isolate the effects of various theoretical and observational
uncertainties on our results. Of those uncertainties, the scatter in the
Faber-Jackson relation and error in the group centroid position dominate.
Future surveys of lens environments should prioritize spectroscopic sampling of
both the local lens environment and objects along the line of sight,
particularly those bright (I < 21.5) galaxies projected within 5' of the lens.
