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 phenomenological Woods-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.