Strong lensing of GW sources makes it possible to constrain the proper transverse velocity of the source, as each lensed image essentially allow the observer to see the source from different sightlines. If the GW source is moving, the different images will therefore show different doppler shifts of the same source, which can be used to triangulate for the velocity vector of the source in the source-plane. I will describe how this works, and illustrate that Einstein Telescope and Cosmic Explorer should be able to infer the transverse velocity of BBH mergers up to redshift 3-4, which has widespread implications for GW science as well as cosmology.