  We construct a new class of 4-dimensional z=2 Lifshitz black branes that have
a nonzero linear momentum. These are solutions of an Einstein-Proca-dilaton
model that can be obtained by Scherk-Schwarz circle reduction of AdS_5 gravity
coupled to a free real scalar field. The boundary of a bulk Lifshitz space-time
is a Newton-Cartan geometry. We show that the fluid dual to the moving Lifshitz
black brane leads to a novel form of Lifshitz hydrodynamics on a Newton-Cartan
space-time. Since the linear momentum of the black brane cannot be obtained by
a boost transformation the velocity of the fluid or rather, by boundary
rotational invariance, its magnitude plays the role of a chemical potential.
The conjugate dual variable is mass density. The Lifshitz perfect fluid can be
thought of as arising from a Schroedinger perfect fluid with broken particle
number symmetry.
