  We study the statistics of large-separation gravitational lens systems
produced by non-spherical halos in the Cold Dark Matter (CDM) model.
Specifically, we examine how the triaxiality of CDM halos affects the overall
lensing probabilities and the relative numbers of different image
configurations (double, quadruple, and naked cusp lenses). We find that
triaxiality significantly enhances lensing probabilities by a factor of ~2-4,
so it cannot be ignored. If CDM halos have central density slopes alpha<~1.5,
we predict that a significant fraction (>~20%) of large-separation lenses
should have naked cusp image configurations; this contrasts with lensing by
isothermal (\alpha~2) galaxies where naked cusp configurations are rare. The
image multiplicities depend strongly on the inner density slope \alpha: for
\alpha=1, the naked cusp fraction is >~60%; while for \alpha=1.5, quadruple
lenses are actually the most probable. Thus, the image multiplicities in
large-separation lenses offer a simple new probe of the inner density profiles
of dark matter halos. We also compute the expected probabilities and image
multiplicities for lensed quasars in the Sloan Digital Sky Survey, and argue
that the recent discovery of the large-separation quadruple lens SDSS
J1004+4112 is consistent with expectations for CDM.
