  We study the flow equations of the shear response functions for hyperscaling
violating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating
exponents $z$ and $\theta$. Adapting the membrane paradigm approach of
analysing response functions as developed by Iqbal and Liu, we focus
specifically on the shear gravitational modes which now are coupled to the
perturbations of the background gauge field. Restricting to the zero momenta
sector, we make further simplistic assumptions regarding the hydrodynamic
expansion of the perturbations. Analysing the flow equations shows that the
shear viscosity at leading order saturates the Kovtun-Son-Starinets (KSS) bound
of $\frac{1}{4\pi}$. When $z=d_i-\theta$, ($d_i$ being the number of spatial
dimension in the dual field theory) the first-order correction to shear
viscosity exhibits logarithmic scaling, signalling the emergence of a scale in
the UV regime for this class of hvLif theories. We further show that the
response function associated to the gauge field perturbations diverge near the
boundary when $z>d_i+2-\theta$. This provides a holographic understanding of
the origin of such a constraint and further vindicates results obtained in
previous works that were obtained through near horizon and quasinormal mode
analysis.
