  We implement Wilson fermions on 2D Lorentzian triangulation and determine the
spectrum of the Dirac-Wilson operator. We compare it to the spectrum of the
corresponding operator in the Euclidean background. We use fermionic particle
to probe the fractal properties of Lorentzian gravity coupled to $c=1/2$ and
$c=4$ matter. We numerically determine the scaling exponent of the mass gap $M
\sim N^{-1/d_H}$ to be $d_H=2.11(5)$, and $d_H=1.77(3)$ for $c=1/2$ and $c=4$,
respectively
