  The lensing cross section of triaxial halos depends on the relative
orientation between a halo's principal axes and its line of sight.
Consequently, a lensing subsample of randomly oriented halos is not, in
general,randomly oriented. Using an isothermal mass model for the lensing
galaxies and their host halos, we show that the lensing subsample of halos that
produces doubles is preferentially aligned along the lines of sight, whereas
halos that produce quads tend to be projected along their middle axes. These
preferred orientations result in different projected ellipticity distributions
for quad, doubles, and random galaxies. We show that ~300 lens systems must be
discovered to detect this effect at the 95% confidence level. We also
investigate the importance of halo shape for predicting the quad-to-double
ratio and find that the latter depends quite sensitively on the distribution of
the short-to-long axis ratio, but is otherwise nearly independent of halo
shape. Finally, we estimate the impact of the preferred orientation of lensing
galaxies on their projected substructure mass fraction, and find that the
observed alignment between the substructure distribution and the mass
distribution of halos result in a negligible bias.
