High-resolution CTIO 4 m/HYDRA spectroscopy of the super-metal-rich open cluster NGC 6253 ([Fe/H] = +0.43 +/- 0.01) has been used to study the stellar lithium (Li) abundances near the cluster's turnoff. NGC 6253 greatly expands the range of [Fe/H] for clusters that have a Li abundance analysis. This is important for studying the complicated effects of, and potential correlations with, stellar Fe abundance on surface Li abundance. Comparisons to the younger and less-metal-rich Hyades and to the similarly aged but solar-metallicity M67 show that NGC 6253's Li abundances are qualitatively consistent with the prediction, from Standard Stellar Evolution Theory, that higher-metallicity stars have a greater Li depletion. Comparison with M67 provides evidence that the more-metal-rich NGC 6253 had a higher initial Li, which is consistent with expectations from models of Galactic Li production. NGC 6253 is also compared to the intermediate-aged NGC 3680, NGC 752, and IC 4651 open clusters. Comparison of the Li-gap positions in all six clusters shows that (1) the gap's position in T-eff is independent of metallicity, but (2) higher-metallicity clusters have their gaps in higher-mass stars. In addition, the Li gap's position is shown not to evolve with age, which provides an important constraint for the non-standard depletion mechanisms that may create the Li gap.