  We show that Zwei-Dreibein Gravity (ZDG), a bigravity theory recently
proposed by Bergshoeff, de Haan, Hohm, Merbis, and Townsend in Phys.Rev.Lett.
111 (2013) 111102, admits exact solutions with anisotropic scale invariance.
These type of geometries are the three-dimensional analogues of the spacetimes
which were proposed as gravity duals for condensed matter systems. In
particular, we find Schr\"odinger invariant spaces as well as Lifshitz spaces
with arbitrary dynamical exponent $z$. We also find black holes that are
asymptotically Lifshitz with $z=3$, showing that these (non-constant curvature)
solutions of New Massive Gravity (NMG) are persistent after the introduction of
the infinite tower of higher-curvature terms of ZDG, provided a renormalization
of the parameters. Black holes in asymptotically warped Anti-de Sitter spaces
are also found. Interestingly, in almost all the geometries studied in this
work, the metric associated with the second dreibein turns out to be
equivalent, up to a constant global factor, to the first one. This phenomenon
has been previously observed in other bigravity theories in asymptotically flat
and asymptotically Anti-de Sitter backgrounds. However, for the particular case
of the $z=3$ Lifshitz black hole, here we found that the second metric
corresponds to a different black hole that coincides with the former only in
the asymptotic region. In fact, we find a new family of $z=3$ black holes that
corresponds to a one-parameter deformation of the NMG solution.
