Static high pressure lithium amide (LiNH2) crystal structures are predicted using evolutionary structure search methodologies and intuitive approaches. In the process, we explore the relationship of the structure and properties of solid LiNH2 to its molecular monomer and dimer, as well as its valence-isoelectronic crystalline phases of methane, water, and ammonia all under pressure. A NaNH2 (Fddd) structure type is found to be competitive for the ground state of LiNH2 above 6 GPa with the P = 1 atm I (4) over bar phase. Three novel phases emerge at 11 (P (4) over bar2,m), 13 (P4(2)/ncm), and 46 GPa (P2(1)2(1)2(1)), still containing molecular amide anions, which begin to form N-H center dot center dot center dot N hydrogen bonds. The P2(1)2(1)2(1) phase remains stable over a wide pressure range. This phase and another Pmc2(1) structure found at 280 GPa have infinite center dot center dot center dot(H)N center dot center dot center dot H center dot center dot center dot N(H)center dot center dot center dot H polymeric zigzag chains comprising symmetric N center dot center dot center dot H center dot center dot center dot N hydrogen bonds with one NH bond kept out of the chain, an interesting general feature found in many of our high pressure (>280 GPa) LiNH2 structures, with analogies in high pressure H2O-ices. All the predicted low enthalpy LiNH2 phases are calculated to be enthalpically stable with respect to their elements but resist metallization with increasing pressure up to several TPa. The possibility of Li sublattice melting in the intermediate pressure range structures is raised.