The dynamics and kinetics of the Li + H-2(+) reaction and its isotopic variants (D-2(+) and T-2(+)) have been studied by using a time dependent wave packet (TDWP) coupled-channel (CC) method on the ab initio potential energy surface (PES) of Martinazzo et al. [J. Chem. Phys. 2003; 119, 21]. Total initial nu = 0, j = 0 state selected reaction probabilities for the Li + H-2(+) reaction and its isotopic variants have been calculated from the threshold up to 1 eV for total angular momenta J from 0 to 90. Integral cross sections have been evaluated from the reaction probabilities at collision energies from threshold (approximate to 0.2 eV) up to 1.0 eV collision. The calculated rate constants a's a function of temperature show an Arrhenius type behavior in the 200 <= T <= 1000 K temperature interval. It has been found to be a considerable large intermolecular kinetic isotope effect. The TDWP-CC results are in overall good agreement with those obtained applying the TDWP Centrifugal-Sudden (CS) approximation, showing that the CS approximation is rather accurate for the title reaction.