  We propose a new model-independent measurement strategy for the propagation
speed of gravitational waves (GWs) based on strongly lensed GWs and their
electromagnetic (EM) counterparts. This can be done in two ways: by comparing
arrival times of GWs and their EM counterparts and by comparing the time delays
between images seen in GWs and their EM counterparts. The lensed GW-EM event is
perhaps the best way to identify an EM counterpart. Conceptually, this method
does not rely on any specific theory of massive gravitons or modified gravity.
Its differential setting (i.e., measuring the difference between time delays in
GW and EM domains) makes it robust against lens modeling details (photons and
GWs travel in the same lensing potential) and against internal time delays
between GW and EM emission acts. It requires, however, that the theory of
gravity is metric and predicts gravitational lensing similar to general
relativity. We expect that such a test will become possible in the era of
third-generation gravitational-wave detectors, when about 10 lensed GW events
would be observed each year. The power of this method is mainly limited by the
timing accuracy of the EM counterpart, which for kilonovae is around $10^4$
s.Thisuncertaintycanbesuppressedbya factor of $\sim 10^{10}$, if strongly
lensed transients of much shorter duration associated with the GW event can be
identified. Candidates for such short transients include short gamma-ray burst
and fast radio bursts.
