  Strong lensing of gravitational waves is more likely for distant sources but
predicted event rates are highly uncertain with many astrophysical origins
proposed. Here we open a new avenue to estimate the event rate of strongly
lensed systems by exploring the amplitude of the stochastic gravitational wave
background (SGWB). This method can provide a direct upper bound on the high
redshift binary coalescing rates, which can be translated into an upper bound
on the expected rate of strongly lensed systems. We show that from the ongoing
analysis of the Laser Interferometer Gravitational-wave Observatory
(LIGO)-Virgo and in the future from the LIGO-Virgo design sensitivity stringent
bounds on the lensing event rate can be imposed using the SGWB signal.
Combining measurements of loud gravitational wave events with an unresolved
stochastic background detection will improve estimates of the numbers of lensed
events at high redshift. The proposed method is going to play a crucial in
understanding the population of lensed and unlensed systems from gravitational
wave observations.
