Based on five different nonempirical (calculated ab initio) interaction potentials for pairs of colliding Li-Ne particles and three different interaction potentials for pairs of colliding Li-Ar particles, we have theoretically investigated the spectral features of the light-induced drift (LID) rate of Li atoms in the buffer Ne gas in a mixture of buffer Ne + Ar gases. The calculations of LID of Li atoms in the buffer Ne gas for two interaction potentials predict anomalous LID and, as a result, strong sensitivity of the spectral shape of the LID lines to the differences in these potentials. For three other potentials (out of the five in question), the shape of the LID line of Li atoms in Ne is insensitive to the shape of the potential, since calculations with these potentials predict a normal LID effect. In this case, as it turned out, by adding a small fraction (approximately 10%) of Ar to Ne, one can go from normal LID to anomalous LID and thereby radically increase the sensitivity of the LID line shape of Li atoms to the difference in these interaction potentials. The results obtained enable high-precision testing of the interatomic interaction potentials in experiments on anomalous LID.