Can I raytrace gravitational lensing using only a single point source of gravity?
As you have probably observed, in general, you cannot solve in closed-form the equations for ray trajectories around multiple distorting objects.

The standard approach for such things is just to discretize it.  This looks like Eulerian integration.  Just step your ray a little bit toward the object, calculate gravity from all sources and bend it, then step it more, und so weiter.  This is called raymarching.

Since you're interested in problems on an astrophysical scale, you can assume the ray is linear far enough away from the object, with minimal error.



Here's a scene I rendered a while ago using a homebrew photonmapper (no QMC) using this raymarching technique.

I present: relativistic photon mapping: black hole in a Cornell box!