The lattice vibrational modes of spinel-structured lithium manganese oxides have been calculated using atomistic modeling methods. The simulations allow the Raman and infrared spectra of lithiated, fully delithiated, and partially delithiated phases to be assigned for the first time. Calculations for the spinels LiMn2O4, lambda-MnO2, and Li0.5Mn2O4 are compared with experimental Raman data measured for thin films of the oxides coated on a platinum electrode. The appearance of a number of new bands in the Raman spectrum of LiMn2O4 following partial extraction of lithium is shown to result from local lowering of the symmetry and Raman activation of modes which are optically inactive or only infrared active in LiMn2O4. The results support a model for the Li0.5Mn2O4 lattice in which the lithium ions are ordered. The deformation vibrations of lattice hydroxyl "defects" in lambda-MnO2 have also been calculated; comparison of the calculated and experimental vibrational data supports a model in which hydroxyl species are localized at octahedral Mn vacancies.