  We develop a formalism with two different UV cutoff scales, one for space and
one for time, appropriate for the richer structure of non-Lorentz invariant
quantum field theories. In this formalism there are two different
beta-functions for each coupling constant, arising from independent variations
of the energy or momentum cutoffs. For holographic non-relativistic theories
with rotational invariance, we develop the technique to calculate such
beta-functions using a generalization of the superpotential formalism developed
in [JHEP ${\bf 1208}$, 164 (2012)]. We then proceed and compute the
beta-function around a Lifshitz critical point, as well as for general
Lifshitz-invariant theories with hyperscaling violation. Finally, we do a
similar computation in a weakly-coupled Lifshitz invariant QFT.
