Elastic scattering angular distribution measurements of the weakly bound ^6,7Li projectiles on a ²³²Th target have been carried out at different bombarding energies close to the Coulomb barrier. The data have been analyzed for both systems using the optical model ECIS code with phenomenologicalWoods-Saxon and Sao Paulo double-folding forms of the optical potentials. The energy dependence of the volume-type real and imaginary parts of the optical potentials are derived from the best fit of the experimental angular distribution data. The usual threshold anomaly has been observed for the ⁷Li + ²³²Th system, whereas there is an indication of a breakup threshold anomaly in case of the ⁶Li + ²³²Th system. Results on total reaction cross sections obtained from the optical model analysis for both systems have been interpreted to understand the role of projectile breakup on the reaction mechanism.