Open clusters (OC) of 1-3 Gyr age contain intermediate-to-low-mass stars in evolutionary phases of multiple relevance to understanding Li evolution. Stars leaving the main sequence (MS) from the hot side of the Lithium dip (LD) at a fixed age can include a range of mass, varying degrees of core degeneracy, and helium ignition under quiescent or flash conditions. An ongoing survey of a significant sample of stars from the giant branch to below the LD in key open clusters has revealed patterns that supply critical clues to the underlying source of Li variation among stars of differing mass and age. While the LD is well established in OC of this age, stars on the hot side of the LD can exhibit Li ranging from the apparent primordial cluster value to upper limits similar to those found at the LD center, despite occupying the same region of the color-magnitude diagram (CMD). Stars on the first-ascent giant branch show a dramatic decline in measurable Li that correlates strongly with increasing age and reduced turnoff mass. We discuss how these trends can be explained in the context of the existence of the LD itself and the temporal evolution of individual stars.