A matrix isolation IR study of laser-ablated lithium atom reactions with H2 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.