Structure quality of LuFeO3 epitaxial layers grown by pulsed-laser deposition on sapphire substrates with and without platinum interlayers has been investigated by in-situ high-resolution x-ray diffraction (reciprocal-space mapping). The parameters of the structure such as size and misorientation of mosaic blocks have been determined as functions of the thickness of LuFeO3 during the PLD growth and for different platinum interlayers thicknesses up to 40 nm. The x-ray diffraction results combined with ex-situ scanning electron microscopy and high-resolution transmission electron microscopy demonstrate that the Pt interlayer significantly improves the structure of LuFeO3 by reducing the misfit of the LuFeO3 lattice with respect to the material underneath.