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Despite the extensive study of lithium depletion during pre-main-sequence (PMS) contraction, studies of individual stars show discrepancies between ages determined from the Hertzsprung-Russell (H-R) diagram and ages determined from lithium depletion, indicating open questions in the PMS evolutionary models. To further test these models, we present high-resolution spectra for members of the β Pictoris Moving Group (BPMG), which is young and nearby. We measure equivalent widths of the 6707.8 Å Li I line in these stars and use them to determine lithium abundances. We combine the lithium abundance with the predictions of PMS evolutionary models in order to calculate a lithium depletion age for each star. We compare this age to the age predicted by the H-R diagram of the same model. We find that the evolutionary models underpredict the amount of lithium depletion for the BPMG given its nominal H-R diagram age of ~12 Myr, particularly for the mid-M stars, which have no observable Li I line. This results in systematically older ages calculated from lithium depletion isochrones than from the H-R diagram. We suggest that this discrepancy may be related to the discrepancy between measured M-dwarf radii and the smaller radii predicted by evolutionary models.