High pressure and high temperature properties of AB (A = 6 Li, 7 Li; B = H, D, T) are investigated with first-principles method comprehensively. It is found that the H − sublattice features in the lowpressure electronic structure near the Fermi level of LiH are shifted to that dominated by the Li + sublattice in compression. The lattice dynamics is studied in quasi-harmonic approximation, from which the phonon contribution to the free energy and the isotopic effects are accurately modelled with the aid of a parameterized double-Debye model. The obtained equation of state (EOS) matches perfectly with available static experimental data. The calculated principal Hugoniot is also in accordance with that derived from shock wave experiments. Using the calculated principal Hugoniot and the previous theoretical melting curve, we predict a shock melting point at 56 GPa and 1923 K. In order to establish the phase diagram for LiH, the phase boundaries between the B1 and B2 solid phases are explored. The B1-B2-liquid triple point is determined at about 241GPa and 2413 K. The remarkable shift in the phase boundaries by isotopic effect and temperature reveal the significant role played by lattice vibrations. Furthermore, the Hugoniot of the staticdynamic coupling compression is assessed. Our EOS suggests that a precompression of the sample to 50 GPa will allow the shock Hugoniot passing through the triple point and entering the B2 solid phase. This transition leads to a discontinuity with 4.6% volume collapse, about four times greater than the same B1-B2 transition at zero temperature.PACS numbers: 63.20.dk, 64.60.A-, 64.70.D-As the lightest ionic compound, as well as the highest mass content of hydrogen and the highest melting point of 965 K at ambient pressure 1 in alkali metal hydrides, LiH has been widely studied and applied in the fields of hydrogen storage 2 , thermonuclear fusion, and aviation and space industries 3-6 . Early static compression experiment using diamond anvil cell (DAC) showed that LiH occupies an FCC lattice and orders in NaCl (B1) structure at ambient condition, and this structure is maintained up to at least 36 GPa (96 GPa for LiD) 7 . Under this pressure, all other alkali hydrides were observed to transform into CsCl (B2) phase (NaH at 29.3 GPa, KH at 4.0 GPa, RbH at 2.2 GPa, CsH at 0.83 GPa) 8-10 . However, the same structural transition in LiH has yet to be observed, which stimulates broad and continuous high pressure experimental and theoretical researches. Recently, by analyzing the x-ray diffraction (XRD) data obtained in DAC experiment 11 , it was shown that at room temperature LiH remains in the B1 structure under pressures up to 252 GPa, the highest pressure having been studied experimentally so far. In particular, the diffraction and Raman data indicated that the B1-B2 phase transition, as well as the accompanied metallization, may not be far beyond 252 GPa 11 .With theoretical methods, the pressure-induced B1-B2 structural transition and the insulator-metal transition in LiH at low temperat...