  Strong lensing of gravitational waves (GWs) is attracting growing attention
of the community. The event rates of lensed GWs by galaxies were predicted in
numerous papers, which used some approximations to evaluate the GW strains
detectable by a single detector. The joint-detection of GW signals by a network
of instruments will increase the detecting ability of fainter and farther GW
signals, which could increase the detection rate of the lensed GWs, especially
for the 3rd generation detectors, e.g., Einstein Telescope (ET) and Cosmic
Explorer (CE). Moreover, realistic GW templates will improve the accuracy of
the prediction. In this work, we consider the detection of galaxy-scale lensed
GW events under the 2nd, 2.5th, and 3rd generation detectors with the network
scenarios and adopt the realistic templates to simulate GW signals. Our
forecast is based on the Monte Carlo technique which enables us to take Earth's
rotation into consideration. We find that the overall detection rate is
improved, especially for the 3rd generation detector scenarios. More precisely,
it increases by ~37% adopting realistic templates, and under network detection
strategy, further increases by ~58% comparing with adoption of the realistic
templates, and we estimate that the 3rd generation GW detectors will detect
hundreds lensed events per year. The effect from the Earth's rotation is
weakened in the detector network strategy.
