The determination of Li and proton-capture element abundances in globular cluster (GC) giants allows us to constrain several key questions on the multiple population scenarios in GCs, from formation and early evolution to pollution and dilution mechanisms. In this Letter, we present our results on Li abundances for a large sample of giants in the intermediate-metallicity GC NGC 6121 (M4), for which Na and O have been already determined by Marino et al. The stars analyzed are both below and above the red giant branch bump luminosity. We found that the first and second generation stars share the same Li content, suggesting that a Li production must have occurred. This provides strong observational evidence supporting the scenario in which asymptotic giant branch stars are GC polluters.