  We consider a covariant formulation of field theories with Lifshitz scaling,
and analyze the energy-momentum tensor and the scale symmetry Ward identity. We
derive the equation of state and the ideal Lifshitz hydrodynamics in agreement
with arXiv:1304.7481, where they were determined by using thermodynamics and
symmetry properties. We construct the charged ideal Lifshitz hydrodynamics in
the generating functional framework as well as in the gravitational holographic
dual description. At the first viscous order, an analysis of the entropy
current reveals two additional transport coefficients (one dissipative and one
dissipationless) compared to the neutral case, contributing to the charge
current and to the asymmetric part of the energy-momentum tensor.
