While I don't have my Astronomers license, I'll start the ball rolling for this really interesting question!
Is it theoretically possible to see a spiral galaxy head on, and side on, if there is a convenient gravitational lensing effect?
Photons via lensing
- It certainly depends on what the definition of "see" is. Astronomers are famous for squeezing out every drop of information available from even a meagre drizzle of photons; Astronomy doesn't depend exclusively on high resolution images.
- Gravitational lensing can bend light through arbitrarily large angles, see for example answers to
This won't be a complete answer, but certainly it is possible to receive at least a stream of photons at Earth from both the edge-on and axial direction if at least one (or two) sufficiently strong gravitational lensing bodies happen to be in the right place.
Photons via scattering
Dust and (to some extent) gas can scatter light. It is not impossible that an extended object can be illuminated by axial light from an edge-on galaxy and scatter some of that towards us. The most likely scenario would probably involve some kind of high energy event or flare from matter falling into a supermassive black hole at the center of the galaxy; the time delay or "echo" between any direct light and the reflected light with a longer path would confirm that the two observed transient events were in fact from the same initial event.