  The diffraction patterns of lensed gravitational waves encode information
about their propagation speeds. If gravitons have mass, the dispersion relation
and speed of gravitational waves will be affected in a frequency-dependent
manner, which would leave traces in the diffraction pattern if the waves are
lensed. In this paper, we study how the alternative dispersion relation induced
by massive gravitons affects gravitational waves lensed by point-mass lenses,
such as intermediate-mass black holes. We find that the waveform morphology of
lensed dispersive gravitational waves depends on the graviton mass more
sensitively than their unlensed counterpart. Together with lensing
amplification, the waveform-morphology modifications due to lensing can improve
the measurement accuracy of the graviton mass. A single lensed
gravitational-wave signal enables us to measure the graviton mass with an
accuracy comparable with the combined measurement across $\mathcal{O}(10^3)$
unlensed signals. Our method allows us to incorporate lensed gravitational-wave
signals into existing graviton-mass measurements. Our method can also be
generalized to other lens types, gravitational-wave sources, and detector
networks, preparing ourselves for thoroughly understanding the nature of
gravitational waves in the era of lensed gravitational-wave astronomy.
