  We present the full charge and energy diffusion constants for the
Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a
dynamical critical exponent $z$. Therein we compute the fully renormalized
static thermodynamic potential explicitly, which confirms the forms of all
thermodynamic quantities including the Bekenstein-Hawking entropy and
Smarr-like relationship. Our exact computation demonstrates a modification to
the Lifshitz Ward identity for the EMD theory. For transport, we target our
analysis at finite chemical potential and include axion fields to generate
momentum dissipation. While our exact results corroborate anticipated bounds,
we are able to demonstrate that the diffusivities are governed by the
engineering dimension of the diffusion coefficient, $[D]=2-z$. Consequently, a
$\beta$-function defined as the derivative of the trace of the diffusion matrix
with respect to the effective lattice spacing changes sign precisely at $z=2$.
At $z=2$, the diffusion equation exhibits perfect scale invariance and the
corresponding diffusion constant is the pure number $1/d_s$ for both the charge
and energy sectors, where $d_s$ is the number of spatial dimensions. Further,
we find that as $z\to\infty$, the charge diffusion constant vanishes,
indicating charge localization. Deviation from universal decoupled transport
obtains when either the chemical potential or momentum dissipation are large
relative to temperature, an echo of strong thermoelectric interactions.
