  We show that there exists a class of charged BTZ-like black hole solutions in
Lifshitz spacetime with a hyperscaling violating factor. The charged BTZ is
characterized by a charge-dependent logarithmic term in the metric function. As
concrete examples, we give five such charged BTZ-like black hole solutions and
the standard charged BTZ metric can be regarded as a special instance of them.
In order to check the recent proposed universal relations between diffusivity
and the butterfly velocity, we first compute the diffusion constants of the
standard charged BTZ black holes and then extend our calculation to arbitrary
dimension $d$, exponents $z$ and $\theta$. Remarkably, the case $d=\theta$ and
$z=2$ is a very special in that the charge diffusion $D_c$ is a constant and
the energy diffusion $D_e$ might be ill-defined, but $v^2_B\tau$ diverges. We
also compute the diffusion constants for the case that the DC conductivity is
finite but in the absence of momentum relaxation.
