We demonstrate submicron ferroelectric domain engineering in liquid phase epitaxy (LPE) LiNbO3 thin films grown on LiNbO3 and LiTaO3 substrates using a direct-write electron beam poling for waveguide applications. LiNbO3 thin films of several-micron thickness were grown using a flux melt of 20 mol% LiNbO3-80 mol% LiVO3. To engineer domain structures in Z- oriented LPE LiNbO3 films, a direct-write electron beam poling was implemented. It is shown that we can engineer the domain structure of LPE LiNbO3 films by using direct e-beam poling, even though the domain orientations of the film and the substrate are opposite. We also compared e-beam poling behavior in a congruent LiNbO3 single crystal and a LPE LiNbO3 film. Using the same e-beam scan parameters, a much enhanced domain structure is obtained in LPE films. Defect structure and composition effects are also discussed.