  Strong gravitational lensing is a gravitational wave (GW) propagation effect
that influences the inferred GW source parameters and the cosmological
environment. Identifying strongly-lensed GW images is challenging as waveform
amplitude magnification is degenerate with a shift in the source intrinsic mass
and redshift. However, even in the geometric-optics limit, Type-II
strongly-lensed images cannot be fully matched by Type-I (or unlensed) waveform
templates, especially with large binary mass ratios and orbital inclination
angles. We propose to use this mismatch to distinguish individual Type-II
images. Using planned noise spectra of Cosmic Explorer, Einstein Telescope and
LIGO Voyager, we show that a significant fraction of Type-II images can be
distinguished from unlensed sources, given sufficient SNR ($\sim 30$).
Incorporating models on GW source population and lens population, we predict
that the yearly detection rate of lensed GW sources with detectable Type-II
images is 172.2, 118.2 and 27.4 for CE, ET and LIGO Voyager, respectively.
Among these detectable events, 33.1%, 7.3% and 0.22% will be distinguishable
via their Type-II images with a log Bayes factor larger than 10. We conclude
that such distinguishable events are likely to appear in the third-generation
detector catalog; our strategy will significantly supplement existing strong
lensing search strategies.
