Search for lithium-rich giants in 32 open clusters with high-resolution spectroscopy

Context. Lithium-rich giant stars are rare and their existence poses a challenge to our understanding of stellar structure and evolution. In particular, open clusters aptly constrain the mass and age of their members, offering a unique opportunity to understand the evolutionary stage where Li enrichment occurs. Aims. We take advantage of the high-quality sample gathered for the search for planets in open clusters with HARPS and UVES to look for Li-rich giants and to identify the Li enrichment mechanisms responsible. Methods. We derived stellar parameters for 247 stars belonging to 32 open clusters, with 0.07 Ga < ages < 3.6 Ga. We employed the spectral synthesis technique code FASMA for the abundance analysis of 228 stars from our sample. We also determined the ages, distances, and extinction using astrometry and photometry from Gaia and PARSEC isochrones to constrain their evolutionary stage. Our sample covers a wide range of stellar masses from 1 to more than 6 M' where the majority of the masses are above 2 M'. Results. We find 14 canonical Li-rich giant stars that have experienced the first dredge-up. This corresponds to 6% of our total sample, higher than what is typically found for field stars. The majority of the stars (11/14) are located at the red clump, two lie on the red giant branch, and we could not conclude on its evolutionary stage for one. Apart from the canonical limit, we used the maximum Li abundance of the progenitor stars as a criterion for Li enrichment and found 12 Li enriched stars (five appearing in the red clump, five at the upper red giant branch, and two that are inconclusive). We find Li enhancement also among eight stars that have passed the first dredge-up and show strong Li lines based on the fact that stars at the same evolutionary stage in the same cluster have significantly different Li abundances. We confirm that giants with higher Li abundances correspond to a higher fraction of fast-rotating giants, suggesting a connection between Li enhancement and stellar rotation, as predicted by stellar models. Conclusions. Our Li-rich giants are found in various evolutionary stages, implying that no unique Li production mechanism is responsible for Li enrichment. Instead, there are different intrinsic or external mechanisms that are simultaneously at play.