  For a generic lattice Hamiltonian of the electron states in Weyl materials,
we calculate analytically the chiral (or, equivalently, valley) charge and
current densities in the first order in background electromagnetic and
strain-induced pseudoelectromagnetic fields. We find that the chiral response
induced by the pseudoelectromagnetic fields is not topologically protected.
Although our calculations reproduce qualitatively the anomalous chiral Hall
effect, the actual result for the conductivity depends on the definition of the
chirality as well as on the parameters of the lattice model. In addition, while
for the well- separated Fermi surfaces surrounding the individual Weyl nodes
the current induced by the magnetic field coincides almost exactly with the
current of the chiral separation effect in linearized models, there are clear
deviations when the Fermi surfaces undergo the Lifshitz transition. In general,
we find that all chiral response coefficients vanish at large chemical
potential.
