  We study the effects of gravitational lensing on neutrino oscillations in the
$\gamma$-spacetime which describes a static, axially-symmetric and
asymptotically flat solution of the Einstein's field equations in vacuum. Using
the quantum-mechanical treatment for relativistic neutrinos, we calculate the
phase of neutrino oscillations in this spacetime by considering both radial and
non-radial propagation. We show the dependence of the oscillation probability
on the absolute neutrino masses, which in the two-flavor case also depends upon
the sign of mass squared difference, in sharp contrast with the well-known
results of vacuum oscillation in flat spacetime. We also show the effects of
the deformation parameter $\gamma$ on neutrino oscillations and reproduce
previously known results for the Schwarzschild metric. We then extend these to
a more realistic three flavors neutrino scenario and study the effects of the
parameter $\gamma$ and the lightest neutrino mass while using best fit values
of neutrino oscillation parameters.
