An analytical potential energy surface is developed from high quality ab initio calculations for the electrostatic region of the Li-+H-2 interaction. The Li-(H-2) electrostatic complex is found to have a linear minimum energy structure with a D-e of 64.44 cm(-1). A numerical determination of the bound levels supported by this potential indicates a D-0 of only about 7 cm(-1) for Li-(para H-2) and a considerably larger D-0 of about 22 cm(-1) for Li-(ortho H-2). Altogether, the Li-(para H-2) interaction is predicted to support 11 bound levels: nu(3)=0, J=0-6; and nu(3)=1, J=0-3, whereas the Li-(ortho H-2) interaction is predicted to support 28 bound levels: nu(3)=0, J=0-10; nu(3)=1, J=0-8; nu(3)=2, J=0-5; and nu(2)=1, J=1-2. Analogous results for the D-2 and HD isotopolouges are reported.