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Accurate quantum reactive calculations for the reaction Li + HD + ( v = 0 , 1 , j = 0) have been performed on the potential energy surface of Martinazzo et al. [J. Chem. Phys. 119 (21), 11241 (2003)] with the time-dependent wave packet coupled-channel approach. The reaction probabilities reveal that the Coriolis coupling effect is significant to the title reaction particularly for the larger mass product LiD. The total differential cross-sections for LiH and LiD indicate that vibrational and translational excitation of HD + stimulate products scatter in the forward regions. For the v = 0 reaction, the products LiH and LiD in low vibrational states show pronounced sideways scattering, while products in higher vibrational states scatter preferentially towards forward/backward regions. For the v = 1 reaction, the scattering in the forward regions is more intense than in the backward regions for both products in each vibrational state. An analysis of the total and state-resolved opacity functions reveal that the reactivity of the title reaction is promoted by high J collisions, and that the angular distributions of the products correlate strongly with low and high J values. [ABSTRACT FROM AUTHOR]