  Gravitational lensing of a quasar by a spiral galaxy should often be
accompanied by damped Lyman-alpha absorption and dust extinction due to the
intervening gaseous disk. In nearly edge-on configurations, the surface mass
density of the gas and stars in the disk could by itself split the quasar image
and contribute significantly to the overall lensing cross section. We calculate
the lensing probability of a disk+halo mass model for spiral galaxies,
including cosmic evolution of the lens parameters. A considerable fraction of
the lens systems contains two images with sub-arcsecond separation, straddling
a nearly edge-on disk. Because of that, extinction by dust together with
observational selection effects (involving a minimum separation and a maximum
flux ratio for the lensed images), suppress the detection efficiency of spiral
lenses in optical wavebands by at least an order of magnitude. The missing
lenses could be recovered in radio surveys. In modifying the statistics of
damped Lyman-alpha absorbers, the effect of extinction dominates over the
magnification bias due to lensing.
