Context. The evolution of lithium abundance over a star's lifetime is indicative of transport processes operating in the stellar interior. Aims: We revisit the relationship between lithium content and rotation rate previously reported for cool dwarfs in the Pleiades cluster. Methods: We derive new LiI 670.8 nm equivalent width measurements from high-resolution spectra obtained for low-mass Pleiades members. We combine these new measurements with previously published ones, and use the Kepler K2 rotational periods recently derived for Pleiades cool dwarfs to investigate the lithium-rotation connection in this 125 Myr-old cluster. Results: The new data confirm the correlation between lithium equivalent width and stellar spin rate for a sample of 51 early K-type members of the cluster, where fast rotating stars are systematically lithium-rich compared to slowly rotating ones. The correlation is valid for all stars over the (J-Ks) color range 0.50-0.70 mag, corresponding to a mass range from about 0.75 to 0.90 M⊙, and may extend down to lower masses. Conclusions: We argue that the dispersion in lithium equivalent widths observed for cool dwarfs in the Pleiades cluster reflects an intrinsic scatter in lithium abundances, and suggest that the physical origin of the lithium dispersion pattern is to be found in the pre-main sequence rotational history of solar-type stars. Based on observations made at Observatoire de Haute Provence (CNRS), France, at the Nordic Optical Telescope (IAC), Spain, and at the W. M. Keck Observatory, Hawaii, USA.Full Table B.1 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/613/A63