  The recent detection of gravitational waves (GWs) and electromagnetic (EM)
waves originating from the same source marks the start of a new multi-messenger
era in astronomy. The arrival time difference between the GW and EM signal can
be used to constrain differences in their propagation speed, and thus
gravitational theories. We study to what extent a non-zero time delay can be
explained by gravitational lensing when the line of sight to the source passes
near a massive object. For galaxy scale lenses, this delay becomes relevant for
GWs with frequencies between $10^{-6}$ and $10^{-9}$ Hz, sourced by super
massive binary black-holes. In addition to GWs detectable by Pulsar Timing
Arrays (PTAs), we expect to find also a unique and recognizable EM signal. We
show that the delay between the GW and EM signal can be of the order of days to
months; within reach of future observations. The effect may become important in
future multi-messenger astronomy probing of gravitational propagation and
interactions.
