We did laser pump-probe far-wing scattering experiments to study the photochemical reactions Li*(2p,3p)+H-2--> LiH(v'=1,2,J')+H. We show in this work that the Li(2p)+H-2--> LiH+H reaction takes place when the kinetic energy of the reactants are high enough. We think that the Li(2p)+H-2 collisions take place preferentially in bent near-C-2v geometry and that the LiH2 (2)A' intermediate plays a major role where wide-amplitude internal vibrations eventually result in losing a hydrogen atom from the LiH2 complex. We also have observed the Li(3p)+H-2--> LiH+H reaction. The rotational state distribution of the LiH product for excitation in the red wing is identical to that found in the blue wing region, it does not show any preference to high or low rotational states, and no asymmetry is observed in the reactive to nonreactive branching ratio. We show different possibilities for the reactive and nonreactive collisions and provide a tentative explanation of the reaction mechanism using the highly accurate ab initio potential energy surfaces. We also show that the harpooning model cannot be used to explain the reaction mechanism in the Li*+H-2 collision for all the atomic states from Li(2s) to Li(3d), and that no long range electron transfer occurs from the metal atom to the hydrogen molecule.