  The CPT odd contribution to the effective electromagnetic action deriving
from the vacuum polarization tensor in a large class of fermionic systems
exhibiting Lorentz invariance violation (LIV) is calculated using thermal field
theory methods, focusing upon corrections depending on the chemical potential.
The systems considered exhibit the axial anomaly and their effective actions
are described by axion electrodynamics whereby all the LIV parameters enter in
the coupling $\Theta(x)$ to the unmodified Pontryagin density. A preliminary
application to type-I tilted Weyl semimetals is briefly presented.
