  We consider relativistic fermionic systems in lattice regularization out of
equilibrium. The chiral magnetic conductivity $\sigma_{CME}$ is calculated in
spatially infinite system for the case when the chiral chemical potential
depends on time while the system initially was in thermal equilibrium at small
but nonzero temperature. We find that the frequency dependent
$\sigma_{CME}(\omega)$ for any nonzero $\omega$ both in the limits $\omega \ll
T$ and $\omega \gg T$ is equal to its conventional value $1$ when the lattice
model approaches continuum limit. Notice that $\sigma_{CME} = 0$ for the case
when the chiral chemical potential does not depend on time at all. We therefore
confirm that the limit of vanishing $\omega$ is not regular for the spatially
infinite systems of massless fermions.
