We construct black hole solutions of type IIB supergravity that are holographically dual to anisotropic plasmas arising from deformations of an infinite class of four-dimensional CFTs. The CFTs are dual to AdS5 × X5, where X5 is an Einstein manifold, and the deformations involve the type IIB axion and dilaton, with non-trivial periodic dependence on one of the spatial directions of the CFT. At low temperatures the solutions approach smooth domain wall solutions with the same AdS5 × X5 solution appearing in the far IR. For sufficiently large deformations an intermediate scaling regime appears which is governed by a Lifshitz-like scaling solution. We calculate the DC thermal conductivity and some components of the shear viscosity tensor.