  A Lifshitz black brane at generic dynamical critical exponent $z > 1$, with
non-zero linear momentum along the boundary, provides a holographic dual
description of a non-equilibrium steady state in a quantum critical fluid, with
Lifshitz scale invariance but without boost symmetry. We consider moving
Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the
non-relativistic stress tensor complex of the dual field theory via a suitable
holographic renormalisation procedure. The resulting black brane hydrodynamics
and thermodynamics are a concrete holographic realization of a Lifshitz perfect
fluid with a generic dynamical critical exponent.
