The volume dependent electronic structure of the spinel-type lithium manganese oxides LixMn2O4, x=0,0.5,1, is studied ab initio by employing a full-potential electronic structure method. The electronic structure, total energies, open-circuit voltage, and magnetic moments were obtained for various spin configurations of LixMn2O4 in the cubic spinel structure and the low-temperature orthorhombic structure. The effect of magnetic ordering on the band structure and structural stability has been investigated and an antiferromagnetic ordering proved to be the ground state of the LixMn2O4 spinels. Our calculations show that the manganese majority t2g d band is filled for all LixMn2O4 compounds studied, and the filling of the minority t2g band is expected in the lithiation process. The lithium intercalation potential, bulk modulus, magnetic moments, and optical properties are calculated within the itinerant band approach and are found to be in good agreement with available experimental data, indicating, that the density-functional theory provides reliable electronic structure of the LixMn2O4 system. The effect of the orthorhombic distortion on electronic structure and magnetism of LiMn2O4 was investigated, and our calculations do not show a substantial charge ordering at the structural transition from the cubic spinel to the orthorhombic structure, as proposed earlier. Instead, the low-temperature orthorhombic structure is found to possess the lowest energy via a Jahn-Teller distortion driven by the d band.