Hydrogen-rich compounds are important for understanding the dissociation of dense molecular hydrogen, as well as searching for room temperature Bardeen-Cooper-Schrieffer (BCS) superconductors. A recent high pressure experiment reported the successful synthesis of novel insulating lithium polyhydrides above 130 GPa. However, the results are in sharp contrast to a previous theoretical prediction by the PBE functional that around this pressure range all lithium polyhydrides (LiHn (n = 2-8)) should be metallic. In order to address this discrepancy, we perform an unbiased structure search with first-principles calculation by including the van der Waals interaction that was ignored in the previous prediction to predict the high pressure stable structures of LiHn,, (n = 2-11, 13) up to 200 GPa. We reproduce the previously predicted structures, and further find novel compositions that adopt more stable structures. The van der Waals functional (vdW-DF) significantly alters the relative stability of lithium polyhydrides, arid predicts that the stable stoichiometries for the ground state should be LiH2, and LiH9 at 130-170 GPa, and LiH2, LiH8, and LiH10 at 180-200 GPa. Accurate electronic structure calculation with GW approximation indicates that LiH, LiH2 LiH7, and LiH9 are insulative up to at least 208 GPa, and all other lithium polyhydrides are metallic. The caltulated vibron frequencies of these insulating phases are also in accordance with the experimental infrared (IR) data. This, reconciliation with the experimental observation suggests that LiH2, LiH7, and LiH9 are the possible candidates for lithium polyhydrides synthesized in that experiment. Our results reinstate the credibility of density functional theory in the description of H-rich compounds, and demonstrate the importance of considering van der Waals interaction in this class of materials.