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We provide a general algorithm for constructing the holographic dictionaryfor any asymptotically locally Lifshitz background, with or withouthyperscaling violation, and for any values of the dynamical exponents $z$ and$\theta$, as well as the vector hyperscaling violating exponent, that arecompatible with the null energy condition. The analysis is carried out for avery general bottom up model of gravity coupled to a massive vector field and adilaton with arbitrary scalar couplings. The solution of the radialHamilton-Jacobi equation is obtained recursively in the form of a gradedexpansion in eigenfunctions of two commuting operators, which are theappropriate generalization of the dilatation operator for non scale invariantand Lorentz violating boundary conditions. The Fefferman-Graham expansions, thesources and 1-point functions of the dual operators, the Ward identities, aswell as the local counterterms required for holographic renormalization allfollow from this asymptotic solution of the radial Hamilton-Jacobi equation. Wealso find a family of exact backgrounds with $z>1$ and $\theta>0$ correspondingto a marginal deformation shifting the vector hyperscaling violating parameterand we present an example where the conformal anomaly contains the only $z=2$conformal invariant in $d=2$ with four spatial derivatives.

Lifshitz holography: The whole shebang