  Strongly lensed gravitational waves (GWs) from binary coalescence manifest as
repeated chirps from the original merger. At the detectors, the phase of the
lensed GWs and its arrival time differences will be consistent modulo a fixed
constant phase shift. We develop a fast and reliable method to efficiently
reject event pairs that are not-lensed copies and appropriately rank the most
interesting candidates. Our method exploits that detector phases are the best
measured GW parameter, with errors only of a fraction of a radian and
differences across the frequency band that are better measured than the chirp
mass. The arrival time phase differences also avoid the shortcomings of looking
for overlaps in highly non-Gaussian sky maps. Our basic statistic determining
the consistency with lensing is the distance between the phase posteriors of
two events and it directly provides information about the lens-source geometry
which helps inform electromagnetic followups. We demonstrate that for simulated
signals of not-lensed binaries specifically chosen with many coincident
properties so as to trigger false lensing alarms none of the pairs have phases
closer than $3\sigma$, and most cases reject the lensing hypothesis by
$5\sigma$. Looking at the latest catalog, GWTC3, we find that only $6\%$ of the
pairs are consistent with lensing at 99\% confidence level. Moreover, we reject
about half of the pairs that would otherwise favor lensing by their parameter
overlaps and demonstrate good correlation with detailed joint parameter
estimation results. This reduction of the false alarm rate will be of paramount
importance in the upcoming observing runs and the eventual discovery of lensed
GWs. Our code is publicly available and could be applied beyond lensing to test
possible deviations in the phase evolution from modified theories of gravity
and constrain GW birefringence.
