We consider holography for Lifshitz spacetimes with dynamical exponent $z = 1 + epsilon ^2$, where $epsilon$ is small. The holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the $z = 1$ theory. We set up the holographic dictionary for Einstein-Proca models and explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent $z = 1 + epsilon ^2$. Using only QFT arguments we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we provide examples of such deformations. An analytic Lifshitz black brane up to second order in $epsilon$ is constructed. Relation to some top-down construction will be discussed. Based on 1304.7776 and 1306.3344.