Can we see a rotating gravitational lens?

It is known that the rotation of a gravitational lens affects properties of images. We consider an inverse problem: If the lens is dark, can we infer its rotation from the observed images? We find that, up to the first order in the gravitational constant G, a rotating lens is not distinguishable from a non-rotating one. The quadrupole contribution to the deflection angle is also calculated for a general, extended lens object.