  Current constraints on Einstein's weak equivalence principle (WEP) utilize
the observed time delay between correlated particles of astronomical sources.
However, the intrinsic time delay due to particle emission time is impossible
to measure and is simply assumed to be zero in previous studies. Here we
propose a robust method to test WEP for relativistic messengers using strongly
lensed cosmic transients, which can naturally overcome the intrinsic time delay
problem. This can be achieved in two ways: by comparing the time delays between
lensed images seen in different energy bands or in gravitational waves (GWs)
and their electromagnetic (EM) counterparts. The power of our method mainly
depends on the timing accuracy of cosmic transient and the strong lensing time
delay. If the time delay of cosmic transient can be measured with accuracy
about 0.1 s (e.g. gamma-ray bursts), we show that the upper limit on the
differences of the parameterized post-Newtonian parameter $\gamma$ value is
$\Delta \gamma<10^{-7}$ with a one-month strong lensing time delay event. This
accuracy of WEP can be improved by a factor of $10^{7}$, if the lens is galaxy
cluster and the strongly lensed cosmic transients have much shorter duration,
such as fast radio bursts.
