The rotational influence on the eddy-diffusivity tensor Dij for anisotropic turbulence fields is considered in order to explain the lithium decay law during the spin-down process of solar-type stars. Rotation proves to be highly effective in the transfer of chemicals through the solar tachocline (beneath the convection zone) which is assumed to contain only turbulence with horizontal motions. The effect is so strong that the tachocline turbulence must not exceed a limit of ∼10 of the rms velocity in the convection zone in order to let the lithium survive after Gigayears. Such long depletion times can also be explained by a very small rotational influence upon the eddy-diffusion tensor if it is realized with correlation times shorter than 15 min. It is argued that such slow and/or short-living turbulence beneath the convection zone could hardly drive the solar dynamo. In our theory the diffusion remains small for rapid rotation due to the rotational quenching of the turbulence. In young stellar clusters like Pleiades, there should be a (positive) correlation between rotation rate and lithium abundance, where the fastest stars should have maximal lithium. First inspections of the data seem to confirm this finding.