The behaviour of lithium at high metallicity in the Milky Way: Selection effects in the samples and the possible role of atomic diffusion

Aims. We revisit large spectroscopic data sets for field stars from the literature to derive the upper Li envelope in the high metallicity regime in our Galaxy.Methods. We take advantage of Gaia EDR3 data and state-of-the-art stellar models to precisely determine the position of the sample dwarf stars in the Hertzsprung-Russell diagram.Results. The highest Li abundances are found in field metal-rich warm dwarfs from the GALAH survey, located on the hot side of the Li-dip. Their mean Li value agrees with what was recently derived for warm dwarfs in metal-rich clusters, pointing towards a continuous increase of Li up to super-solar metallicity. However, if only cool dwarfs are considered in GALAH, as done in the other literature surveys, it is found that the upper Li envelope decreases at super-solar metallicities, blurring the actual Li evolution picture. We confirm the suggestion that field and open cluster surveys that found opposite Li behaviour in the high metallicity regime do not sample the same types of stars: The first ones, with the exception of GALAH, miss warm dwarfs that can potentially preserve their original Li content.Conclusions. Although we can discard the bending of the Li upper envelope at high metallicity derived from the analysis of cool star samples, we still need to evaluate the effects of atomic diffusion on warm, metal-rich early-F and late-A type dwarfs before deriving the actual Li abundance at high metallicity.