We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. Тhe 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 ε is constructed. Relation to some top-down construction will be discussed. Based on 1304.7776 and 1306.3344.