  We study out-of-equilibrium energy transport in a quantum critical fluid with
Lifshitz scaling symmetry following a local quench between two semi-infinite
fluid reservoirs. The late time energy flow is universal and is accommodated
via a steady state occupying an expanding central region between outgoing shock
and rarefaction waves. We consider the admissibility and entropy conditions for
the formation of such a non-equilibrium steady state for a general dynamical
critical exponent z in arbitrary dimensions and solve the associated Riemann
problem. The Lifshitz fluid with z=2 can be obtained from a Galilean boost
invariant field theory and the non-equilibrium steady state is identified as a
boosted thermal state. A Lifshitz fluid with generic z is scale invariant but
without boost symmetry and in this case the non-equilibrium steady state is
genuinely non-thermal.
