The TbFe2 compound has been deposited by molecular beam epitaxy on lithium niobate (LN) substrates with different orientations (LN Z-, 128 Y- and 41 Y-cuts). Despite the challenging growth on these unconventional substrates, crystalline TbFe2 films (as a single orientated domain or with a limited number of orientations) of reasonable structural quality could be obtained after the deposition of a Mo buffer layer. Detailed and combined RHEED and x-ray analysis permitted to unravel the complex Mo and TbFe2 crystal orientations and to reveal common 3D orientation relationships between the different lattices, whatever the initial LN cut. The magnetic properties and especially the magnetic anisotropy have been investigated in taking magnetocrystalline, magnetoelastic and magnetostatic contributions into account. These promising results on the epitaxial growth of hybrid piezoelectric/magnetostrictive crystalline system constitute an important step towards the control of magnetization via electrically generated static and/or dynamic strains, and towards the development of magnetic sensors based on surface acoustic wave devices.