  Gravitational lensing provides an efficient tool for the investigation of
matter structures, independent of the dynamical or hydrostatic equilibrium
properties of the deflecting system. However, it depends on the kinematic
status. In fact, either a translational motion or a coherent rotation of the
mass distribution can affect the lensing properties. Here, light deflection by
galaxy clusters in motion is considered. Even if gravitational lensing mass
measurements of galaxy clusters are regarded as very reliable estimates, the
kinematic effect should be considered. A typical peculiar motion with respect
to the Hubble flow brings about a systematic error < 0.3%, independent of the
mass of the cluster. On the other hand, the effect of the spin increases with
the total mass. For cluster masses ~ 10^{15}M_{sun}, the effect of the
gravitomagnetic term is < 0.04% on strong lensing estimates and < 0.5% in the
weak lensing analyses. The total kinematic effect on the mass estimate is then
< 1%, which is negligible in current statistical studies. In the weak lensing
regime, the rotation imprints a typical angular modulation in the tangential
shear distortion. This would allow in principle a detection of the
gravitomagnetic field and a direct measurement of the angular velocity of the
cluster but the required background source densities are well beyond current
tecnological capabilities.
