  The Dirac equation is solved in the $z=0$ Lifshitz black hole ($Z0$LBH)
spacetime. The set of equations representing the Dirac equation in the
Newman-Penrose (NP) formalism is decoupled into a radial set and an angular
set. The separation constant is obtained with the aid of the spin weighted
spheroidal harmonics. The radial set of equations, which is independent of
mass, is reduced to Zerilli equations (ZEs)\ with their associated potentials.
In the near horizon (NH) region, these equations solved in terms of the Bessel
functions of the first and second kinds arising from the fermionic perturbation
on the background geometry. For computing the BQNMs instead of the ordinary
quasinormal modes (QNMs), we first impose the purely ingoing wave condition at
the event horizon. And then, Dirichlet boundary condition (DBC) and Newmann
boundary condition (NBC) are applied in order to get the resonance conditions.
For solving the resonance conditions we follow an iteration method. Finally,
Maggiore's method (MM) is employed to derive the entropy/area spectra of the
$Z0$LBH which are shown to be equidistant.
