  The transport behavior of strongly anisotropic systems is significantly
richer compared to isotropic ones. The most dramatic spatial anisotropy at a
critical point occurs at a Lifshitz transition, found in systems with merging
Dirac or Weyl point or near the superconductor-insulator quantum phase
transition. Previous work found that in these systems a famous conjecture on
the existence of a lower bound for the ratio of a shear viscosity to entropy is
violated, and proposed a generalization of this bound for anisotropic systems
near charge neutrality involving the electric conductivities. The present study
uses scaling arguments and the gauge-gravity duality to confirm the previous
analysis of universal bounds in anisotropic Dirac systems. We investigate the
strongly-coupled phase of quantum Lifshitz systems in a gravitational
Einstein-Maxwell-dilaton model with a linear massless scalar which breaks
translations in the boundary dual field theory and sources the anisotropy. The
holographic computation demonstrates that some elements of the viscosity tensor
can be related to the ratio of the electric conductivities through a simple
geometric ratio of elements of the bulk metric evaluated at the horizon, and
thus obey a generalized bound, while others violate it. From the IR critical
geometry, we express the charge diffusion constants in terms of the square
butterfly velocities. The proportionality factor turns out to be
direction-independent, linear in the inverse temperature, and related to the
critical exponents which parametrize the anisotropic scaling of the dual field
theory.
