  We analytically obtain a new charged Lifshtitz solution by adding a
non-relativistic Maxwell field in Horava-Lifshitz gravity. The black hole
exhibits an anisotropic scaling between space and time (Lifshitz scaling) in
the UV limit, while in the IR limit, the Lorentz invariance is recovered. We
introduce the probed Lorentz-violation fermions into the background and
holographically investigate the spectral properties of the dual fermionic
operator. The Lorentz-violation of fermions will enhance the peak and
corresponds larger fermi momentum, which compensates the non-relativistic bulk
effect of the dynamical exponent. For a fixed $z$, when the Lorentz-violation
of fermions increases to a critical value, the behavior of the low energy
excitation goes from a non-Fermi liquid type to a fermi liquid type, which
implies a kind of phase transition.
