A matrix isolation IR study of laser-ablated lithium atom reactions with H-2 has been performed in solid para-hydrogen, normal hydrogen, neon, and argon. The LiH molecule and (LiH)(2,3,4) clusters were identified by IR spectra with isotopic substitution (HD, D-2, and H-2 + D-2) and comparison to frequencies calculated by density functional theory and the MP2 method. The LiH diatomic molecule is highly polarized and associates additional H-2 to form primary (H-2)(2)LiH chemical complexes surrounded by a physical cage of solid hydrogen where the ortho and para spin states form three different primary complexes and play a role in the identification of the bis-dihydrogen complex and in characterization of the matrix cage. The highly ionic rhombic (LiH)(2) dimer, which is trapped in solid matrices, is calculated to be 22 kcal/mol more stable than the inverse hydrogen bonded linear LiH-LiH dimer, which is not observed here. The cyclic lithium hydride trimer and tetramer clusters were also observed. Although the spontaneous reaction of 2 Li and H-2 to form (LiH)(2) occurs on annealing in solid H-2, the formation of higher clusters requires visible irradiation. We observed the simplest possible chemical reduction of dihydrogen using two lithium valence electrons to form the rhombic (LiH)(2) dimer.