We investigate the epitaxial properties of LiNbO3 films grown by pulsed laser deposition on different single-crystal substrates such as SrTiO3 (100), NdGaO3(110) and MgO(111) by using several X-ray diffraction methods: conventional X-ray diffraction,, X-ray reciprocal space mapping and azimuthal X-ray scans. The different domain structures and mosaic spreads observed for films deposited on different substrates are explained by different crystallographic symmetry of substrate surfaces and by different lattice mismatch values. In particular, the LiNbO3 films grown on NdGaO3 (110) exhibit two twinned crystalline domains which are tilted in a well-defined fashion in order to minimize the strain energy and to accommodate the lattice mismatch between the film and the substrate. The films grown on SrTiO3 (100) show four domains and a larger mosaic spread, while the films grown on MgO(111) are single oriented due to the good lattice accommodation.