The rapidly rotating cool dwarfs of the Pleiades are rich in lithium relative to their slowly rotating counterparts. Motivated by observations of inflated radii in young, active stars, and by calculations showing that radius inflation inhibits pre-main-sequence (pre-MS) Li destruction, we test whether this pattern could arise from a connection between stellar rotation rate and radius inflation on the pre-MS. We demonstrate that pre-MS radius inflation can efficiently suppress lithium destruction by rotationally induced mixing in evolutionary models, and that the net effect of inflation and rotational mixing is a pattern where rotation correlates with lithium abundance for M* < M☉, and anticorrelates with lithium abundance for M* > M☉, similar to the empirical trend in the Pleiades. Next, we adopt different prescriptions for the dependence of inflation on rotation, and compare their predictions to the Pleiades lithium/rotation pattern. We find that if a connection between rotation and radius inflation exists, then the important qualitative features of this pattern naturally and generically emerge in our models. This is the first consistent physical model to date that explains the Li-rotation correlation in the Pleiades. We discuss plausible mechanisms for inducing this correlation and suggest an observational test using granulation.