This question is about how to explain gravitational lensing to a layman, not about exact theoretical correctness.
I am accustomed to explaining optical refraction in terms of wavefronts and the fact that light moves at different speeds in different media. For example, I explain an optical lens by saying
A plane wave that is incident normal to the flat surface of a plano-convex lens will propagate slower inside the lens. This means that the portions of the wavefront that exit the lens first, near the edges, will end up ahead of the portions that exit near the middle of the lens. This results in the wavefronts downstream from the lens having a concave curvature. Because the wave propagates perpendicular to the wavefront, it converges to a point.
I would like to use an analogous explanation to describe the effects of a gravitational lens. Although the local speed of light is invariant in a vacuum, gravity causes the local frequency and wavelength of light in an initially flat, monochromatic, wavefront to vary with radial distance from a gravitating mass. When the light wave has passed far enough downstream from the gravitating mass, the frequency and wavelength return to their original values, but the wavefront is curved because of the changes experienced by different parts of the wavefront while passing through the gravitational field of the mass: the parts of the wavefront near the middle are delayed relative to those near the edges.
I've been trying to refine this explanation, but am running into a complication that, thus far, is beyond my skills. I understand time dilation in terms of gravitational redshift and blueshift. The complication is that both the wavelength and frequency of light (from the perspective of a distant observer) would seem to be affected by the gravitational field. It's not obvious to me how wavelength is affected by gravity. Locally, the wavelength change should balance the frequency change in such a way that the speed of light is $c$. This suggests that the apparent wavelength as judged by a distant observer should also change.
I don't know how to explain this in an intuitively satisfying way, probably because I don't understand well enough how a distant observer can remotely measure the length of something that is deep in a gravitational well. Any help will be greatly appreciated.