  We construct classes of smooth metrics which interpolate from Bianchi
attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or
$AdS_2 \times S^3$ geometries in the UV. While we do not obtain these metrics
as solutions of Einstein gravity coupled to a simple matter field theory, we
show that the matter sector stress-energy required to support these geometries
(via the Einstein equations) does satisfy the weak, and therefore also the
null, energy condition. Since Lifshitz or $AdS_2 \times S^3$ geometries can in
turn be connected to $AdS_5$ spacetime, our results show that there is no
barrier, at least at the level of the energy conditions, for solutions to arise
connecting these Bianchi attractor geometries to $AdS_5$ spacetime. The
asymptotic $AdS_5$ spacetime has no non-normalizable metric deformation turned
on, which suggests that furthermore, the Bianchi attractor geometries can be
the IR geometries dual to field theories living in flat space, with the
breaking of symmetries being either spontaneous or due to sources for other
fields. Finally, we show that for a large class of flows which connect two
Bianchi attractors, a C-function can be defined which is monotonically
decreasing from the UV to the IR as long as the null energy condition is
satisfied. However, except for special examples of Bianchi attractors
(including AdS space), this function does not attain a finite and non-vanishing
constant value at the end points.
