  We study the optical conductivity in a (2+1)-dimensional non-relativistic
field theory holographically dual to a (3+1)-dimensional charged Lifshitz black
brane with the Einstein-Maxwell-dilaton theory. Surprisingly, we find that the
optical AC conductivity satisfies the nontrivial (non-)power law scaling in the
high frequency regime rather than approaching to a constant when the dynamical
critical exponent $z>1$, which is qualitatively similar to those in various
disordered solids in condensed matter systems. Besides, this (non-)power law
scaling behavior shows some universality, which is robust against the
temperatures. We argue that the peculiar scaling behavior of AC conductivity
may stem from the couplings of the dilaton field with the gauge fields and also
the logarithmic behavior near the boundary in the Lifshitz spacetime.
