Do alternate theories for Dark Matter (like MOND) explain its effect on gravitational lensing? For a long time, I was sceptical about the evidence for dark matter. To me, it seemed like a pretty big leap to make when we have no idea whether or not our current models of gravity should apply exactly to cosmological objects of massive scales like galaxies. Just like Einstein’s relativity replaces Newton's laws, wouldn't MOND be a better explanation for the discrepancies of galactic rotations than some "dark matter" that we have no evidence of?
Apparently though, its effect on galactic rotation is not the only evidence of dark matter, we can also see the effect of dark matter on the gravitational lensing of galaxies. That seems a lot harder to explain using modified theories of gravity than the rotational problem.
Do any of the modified theories of gravity address this evidence for dark matter, or just the galactic rotation problem?
 A: Milgrom's simple Newtonian MOND cannot, as it is just a modification of newtonian dynamics (which is the acronym for MOND, after all).  Jacob Bekenstein, however, has worked out a relativistic generalization of MOND called TeVeS that does account for gravitational lensing and a variety of other effects:
https://en.wikipedia.org/wiki/TeVeS
TeVeS is ludicrously complex, though.  And it is unclear whether it can explain effects like the bullet cluster, where gravitating dark matter seperates from normal matter.  Also, one could argue that, in a lot of ways, TeVeS is just a proposal for the dark matter Lagrangian (though it couples to the metric in such a way to mimic gravity).  
A: Milgrom compared MOND predictions to Galaxy-Galaxy Lensing (GGL) data and found reasonable M/L for the lensing galaxies gave good agreement.
"Testing the MOND Paradigm Of Modified Dynamics with Galaxy-Galaxy Gravitational Lensing" (July 21, 2013) https://arxiv.org/abs/1305.3516
Notice that this does not explain the Bullet Cluster where the mass contours from GGL encompass a region with no visible mass.  MOND is said to fail in clusters of galaxies because it predicts an invisible missing mass that is about equal to the visible mass of the cluster.  Newton predicts missing mass ("Dark Matter") that is ~100 times the visible mass of the cluster.
If you fill up the phase space of a galactic cluster (out to ~megaparsec, 1000 km/sec) with a Fermi Dirac distribution of neutrinos (3 generations) and all the neutrinos have ~1 eV mass, then this would explain the MOND predicted invisible missing mass.  This is below the present measured electron neutrino mass limit of 2.2 eV.  KATRIN will soon begin a more sensitive mass measurement down to .2 eV.  CMBR measurements with the DM paradigm strongly disfavor such a large neutrino mass.  There is some chance KATRIN's results will be exciting.
