  We study asymptotically Lifshitz solutions with critical exponent $z \neq 1$
in Horava gravity in three and four spacetime dimensions. For $z=2$ and
$z=3/2$, we find a novel class of numerical solutions with regular universal
horizon, but are characterized by non-analytic behavior near infinity. In the
interior, inside the universal horizon, the unit timelike vector field
associated with the preferred time foliation exhibits oscillatory behavior,
qualitatively similar to that found earlier in asymptotically flat solutions.
For $z>2$ no solutions of this type appear to exist. We comment on potential
applications to holographic Lifshitz dualities.
