Univ Talca, Inst Matemat & Fis, Talca, Chile; Hassaine, M (Hassaine, Mokhtar)Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension D are known only if the dynamical critical exponent is fixed as z = 2(D - 2). In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent z > 1 by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called ( , P )-formalism and obtain a family of charged black hole solutions depending on two parameters. We also remark that the value of the dynamical exponent z = D - 2 turns out to be critical in the sense that it yields asymptotically Lifshitz black holes with logarithmic decay supported by a particular logarithmic electrodynamics. All these configurations include extremal Lifshitz black holes. Charged topological Lifshitz black holes are also shown to emerge by slightly generalizing the proposed electrodynamics.