The heterogeneous equilibria attained during thermal dissociation and hydrogen reduction of LuMnO3 and LuMn2O5 are investigated using the static method (vacuum circulation setup) and X-ray powder diffraction analysis of quenched solid phases. It is found that the dissociation of LuMn2O5 proceeds in three stages. At the low-oxygen boundary of the homogeneity region of LuMn2O5, this compound dissociates into LuMnO3 and Mn3O4 with the liberation of oxygen. Upon reduction, LuMnO3 dissociates with the formation of Lu2O3 and MnO and the liberation of oxygen. Equations for the dissociation and reduction reactions of LuMn2O5 and LuMnO3 are derived, and mass balance equations for these processes are written. A fragment of the isothermal section of the phase diagram of the Lu–Mn–O system at a temperature of 900°C is constructed in the “composition–oxygen pressure” coordinates.