  We study the observational signatures of the lensing signal produced by dark
matter halos with embedded misaligned disks. This issue is of particular
interest at the present time since most of the observed multiple lens systems
have magnification ratios and image geometries that are not well-fit by
standard mass models. The presence of substructure exterior to the lens has
been invoked by several authors in the context of Cold Dark Matter (CDM) models
in order to explain the anamolous magnification ratios. We emphasize that the
anomalous magnification ratios may be an artifact of the simple one-component
mass models currently in use; the inclusion of a misaligned disk may be able to
mimic the effect of substructure. These slight spatial offsets between the dark
matter halo and the disk, which are likely to occur during or as a consequence
of interactions or mergers, lead to complex image configurations and
non-standard magnification ratios. We investigate two illustrative lens models:
a spiral disk embedded within a dark matter halo, and a compact disk-like
component within an elliptical galaxy. The expected fraction of galaxies with a
misaligned disk is estimated to be of the order of 10%. In such cases we find
that the resultant lensing geometries are unusual, with high image
multiplicities. The caustic structures - both radial and tangential - are
drastically modified and the magnification ratios differ compared to
expectations from standard lens models. The additional parameters required to
specify the relative alignment of the mass components in the primary lens
introduce yet another source of uncertainty in the mass modeling of
gravitational lens systems.
