  We study the effects of large-scale density fluctuations on strong
gravitational lensing. Previous studies have focused mostly on weak lensing,
since large-scale structure alone cannot produce multiple images. When a galaxy
or cluster acts as a primary lens, however, we find that large-scale structure
can produce asymmetric shear of the same order as the lens itself. Indeed, this
may explain the origin of the large shear found in lens models in conflict with
the small ellipticity of the observed galaxy light distributions. We show that
large-scale structure changes the lens equation to the form of a generalized
quadrupole lens, which affects lens reconstruction. Large-scale structure also
changes the angular diameter distance at a given redshift. The precise value
depends on the lens and source redshifts and on the large-scale structure power
spectrum, but the induced $1\sigma$ uncertainty in determinations of the Hubble
constant from measurements of time delays is of order $5-10 \%$. If
observations of lensing can constrain the magnitude of the shear which is due
to large-scale structure, it would provide a direct probe of the overall
amplitude of mass fluctuations.
