  We consider holography for Lifshitz spacetimes with dynamical exponent
z=1+epsilon^2, where epsilon is small. We show that the holographically dual
field theory is a specific deformation of the relativistic CFT, corresponding
to the z=1 theory. Treating epsilon as a small expansion parameter we set up
the holographic dictionary for Einstein-Proca models up to order epsilon^2 in
three and four bulk dimensions. We explain how renormalization turns the
relativistic conformal invariance into non-relativistic Lifshitz invariance
with dynamical exponent z=1+epsilon^2. We compute the two-point function of the
conserved spin two current for the dual two-dimensional field theory and verify
that it is Lifshitz invariant. Using only QFT arguments, we show that a
particular class of deformations of CFTs generically leads to Lifshitz scaling
invariance and we construct examples of such deformations.
