A simple system of epitaxial film electrodes with no additives is desirable for investigation surface reactions and anisotropic electrochemical properties of battery's active materials. In this work we demonstrate the possibility of growing epitaxially by pulsed laser deposition single orientation thin films of two phases, orthorhombic o-LiMnO2 and monoclinic m-Li2MnO3; the phases were and still are of great interest for developing high capacity intercalation cathodes for Li-ion batteries. Orientation of the films was controlled by selecting orientation of SrTiO3 substrate covered coherently with a layer of SrRuO3 to provide electrical contact for future electrochemical measurements. Different phases were formed by adjusting temperature of a substrate during deposition, 600 degrees C for forming m-Li2MnO3, and 700-800 degrees C - for o-LiMnO2. Detailed high-resolution scanning transmission electron microscopy of cross-sections has determined the unique orientation relationship for both phases, which can be seen as cube-on-cube of cubic and pseudo-cubic oxygen sub-lattices of SRO and Li-Mn-O phases, respectively. Lower symmetry of the Li-Mn-O phases results in formation of structural domains, which are analyzed in detail. Published by Elsevier B.V.