The full charge density exact muffin-tin orbitals method has been used to study the stability of lithium manganese oxides exhibiting different crystallographic forms. Calculations have been performed in various crystallographic phases of LiMnO2 for the ferromagnetic and antiferromagnetic spin configurations on Mn sublattice, as well as for the state with local moment disorder. For the ordered LiMnO2 compound, the experimentally observed antiferromagnetic orthorhombic ground state structure was reproduced. The effect of doping of the Mn sites by Co was considered with the primary aim to predict the stabilization of the layered structure.