State-to-state quantum dynamics calculations for the H + LiH (v = 0-1, j = 0) -> H-2 + Li reactions are performed based on an ab initio ground electronic state potential energy surface (PES). Total and product state-resolved integral and differential cross sections and rate constants are calculated. The present total integral cross sections and rate constants for the H + LiH (v = 0, = 0) reaction are found to be in agreement with previous literature results. Product state-resolved integral cross sections and rate constants reveal that the H-2 products are preferred to be formed in their rovibrational excited states. The differential cross sections show that the intensity of forward scattering for the H-2 products in their rovibrational excited states is stronger than other states. The mechanisms for the v = 0 and v = 1 reactions are found to be highly consistent with each other. Further, the influence of the stripping mechanism on the H + LiH reaction is studied. It is found that the stripping mechanism could be responsible for the decrease of the reactivity, the product state distribution, and scattering direction of the H-2 products. It is related to the "attractive" feature of the underlying PES.