The optical potential is a key tool for describing interactions in nuclear collisions and is widely used in studies of nuclear reaction mechanisms. The optical potential is highly sensitive to nuclear structure, thereby leading to distinct characteristics between weakly bound and tightly bound nuclear systems. For weakly bound nuclei such as ⁶Li, ⁹Be and ⁶He, the behavior of the optical potential remains controversial due to insufficient experimental data at near-barrier and deep-barrier energies. In this work, elastic scattering angular distributions for the ⁶Li+²⁰⁸Pb system are measured at near-barrier and deep-barrier energies. Optical model fitting is employed to extract the optical potential parameters. The results indicate that there is an anomalous threshold anomaly for the optical potential of this system, so the dispersion relation is not applicable. Furthermore, the reaction threshold for the ⁶Li+²⁰⁸Pb system is determined to be approximately 0.73V_B based on deep-barrier data. A systematic analysis is also performed on the reaction thresholds and breakup thresholds of different nuclear systems. In this work the optical potential of the ⁶Li+²⁰⁸Pb system is measured at near-barrier and deep sub-barrier energies, providing data support for further investigation of the anomalous threshold anomaly. The datasets presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00218.