  We perform electronic structure calculations for the recently synthesized
iron-based superconductor LiFeO$_2$Fe$_2$Se$_2$. In contrast to other
iron-based superconductors, this material comprises two different iron atoms in
3$d^5$ and 3$d^6$ configurations. In band theory, both contribute to the
low-energy electronic structure. Spin-polarized density functional theory
calculations predict an antiferromagnetic metallic ground state with different
moments on the two Fe sites. However, several other almost degenerate magnetic
configurations exist. Due to their different valences, the two iron atoms
behave very differently when local quantum correlations are included through
the dynamical mean-field theory. The contributions from the half-filled 3$d^5$
atoms in the LiFeO$_2$ layer are suppressed and the 3$d^6$ states from the FeSe
layer restore the standard iron-based superconductor fermiology.
