Degeneracy in exotic gravitational lensing

We present three different theoretically foreseen, but unusual, astrophysical situations where the gravitational lens equation ends up being the same, thus producing a degeneracy problem. These situations are: (a) the case of gravitational lensing by exotic stresses (matter violating the weak energy condition and thus having a negative mass, particular cases of wormhole solutions can be used as an example), (b) scalar field gravitational lensing (i.e. when considering the appearance of a scalar charge in the lensing scenario), and (c) gravitational lensing in closed universes (with antipodes). The reasons that lead to this degeneracy in the lens equations, the possibility of actually encountering it in the real universe, and eventually the ways to break it, are discussed.