The crystallographic orientation of epitaxial LiNbO3 films on the Al2O3(1120) substrate can be controlled either toward the c-axis or a-axis depending on the situation at crystallization. Crystallization during high-rate sputter deposition at elevated temperatures produced c-axis-oriented film with 60 degrees-rotated twin domains. Minimizing the surface energy when the growing surface was exposed to abundant ion flux selected (0001) terminated mosaic crystal. In contrast, solid-phase crystallization or as crystallization during a low-rate sputter deposition yielded a-axis-oriented film coexisting with 180 degrees polarization twin domains. The enhanced migration of atoms in low-density amorphous film as well as pseudomorphic lattice matching growth under thermal equilibrated conditions led to the self-organization of relaxed crystalline domains.