  We analyse the power counting renormalizability of the quantum field theory
of Einstein or Einstein-Gauss-Bonnet gravity in D+2 dimensional Lifshitz
spacetime. We show the spectral dimension becomes 2+(D/z) at the UV region
where z is the critical exponent. Since it is larger than two, the quantum
theory of Einstein gravity is not power counting renormalizable. For the pure
Einstein-Gauss-Bonnet gravity, where Lifshitz spacetime is allowed only when
the parameters are fine tuned, it happens that the graviton modes do not
propagate and the quantum field theory is accidentally renormalizable when
z>=D. Another method is discretizing the radial coordinate which changes the
spectral dimension to 1+(D/z) at the UV region. Since our four dimensional
spacetime is continuous, the four dimensional Lorentz symmetry is recovered at
the low energy and the power counting renormalizability is still kept for z>=D,
if the spacetime near the null singularity in Lifshitz spacetime is modified
into AdS spacetime and the discrete radial direction is compactified like a
brane world scenario. We also comment on the AdS/CFT correspondence.
