Elastic-scattering angular distributions for the ^6,7Li + ⁸⁰Se systems were measured at center-of-mass energies from below to above the Coulomb barrier, 13<E_c.m.<24 MeV. The experimental elastic-scattering cross sections were analyzed within the framework of the optical model to study the energy dependence of the real and imaginary parts of the nuclear-interaction potential. The main objective was to investigate the threshold anomaly in those weakly bound systems. The behavior of the calculated potentials as a function of energy indicates that our results are qualitatively consistent with the dispersion relation. The threshold anomaly was observed in the ⁷Li + ⁸⁰Se system and for the ⁶Li + ⁸⁰Se system a breakup threshold anomaly is apparent. An analysis of the absorptive processes, involved in the discussion of the experimental results, was performed using the phenomenological optical potentials that best fit the experimental data.