  When gravitational waves pass near massive astrophysical objects, they can be
gravitationally lensed. The lensing can split them into multiple wave-fronts,
magnify them, or imprint beating patterns on the waves. Here we focus on the
multiple images produced by strong lensing. In particular, we investigate
strong lensing forecasts, the rate of lensing, and the role of lensing
statistics in strong lensing searches. Overall, we find a reasonable rate of
lensed detections for double, triple, and quadruple images at the
LIGO--Virgo--KAGRA design sensitivity. We also report the rates for A+ and LIGO
Voyager and briefly comment on potential improvements due to the inclusion of
sub-threshold triggers. We find that most galaxy-lensed events originate from
redshifts $z \sim 1-4$ and report the expected distribution of lensing
parameters for the observed events. Besides forecasts, we investigate the role
of lensing forecasts in strong lensing searches, which explore repeated event
pairs. One problem associated with the searches is the rising number of event
pairs, which leads to a rapidly increasing false alarm probability. We show how
knowledge of the expected galaxy lensing time delays in our searches allow us
to tackle this problem. Once the time delays are included, the false alarm
probability increases linearly (similar to non-lensed searches) instead of
quadratically with time, significantly improving the search. For galaxy cluster
lenses, the improvement is less significant. The main uncertainty associated
with these forecasts are the merger-rate density estimates at high redshift,
which may be better resolved in the future.
