  We focus on a modified version of Horava - Lifschitz theory and, in
particular, we consider the impact of its weak - field static spherically
symmetric limit on the galaxy dynamics. In a previous paper, we used the
modified gravitational potential obtained in this theory to evaluate the Milky
Way rotation curve using a spheroidal truncated power - law bulge and a double
exponential disc as the only sources of the gravitational field and showed that
the modified rotation curved is not in agreement with the data. Making a step
forward, we here include also the contribution from a dark matter halo in order
to see whether this helps fitting the rotation curve data. As a test case, we
consider a sample of spiral galaxies with smooth baryon matter distribution and
well measured circular velocity profiles. It turns out that, although a
marginal agreement with the data can be found, this can only be obtained if the
dark matter halo has an unrealistically small virial mass and incredibly large
concentration. Such results can be interpreted as a strong evidence against the
reliability of the gravitational potential obtained in the modified version of
Horava -Lifschitz theory that we consider.
