Context. Reconstructing the Galactic evolution of lithium (Li) is the main tool used to constrain the source(s) of Li enrichment in the Galaxy. Recent results have suggested a decline in Li at supersolar metallicities, which may indicate reduced production. Aims. We exploit the unique characteristics of the Gaia-ESO Survey open star cluster sample to further investigate this issue and to better constrain the evolution of Li at high metallicity. Methods. We trace the upper envelope of Li abundance versus metallicity evolution using 18 clusters and considering members that should not have suffered any Li depletion. Results. At variance with previous claims, we do not find any evidence of a Li decrease at high metallicity. The most metal-rich clusters in the sample ([Fe/H] = ∼0.3) actually show the highest Li abundances, with A(Li) > 3.4. Our results clearly show that previous findings, which were based on field stars, were affected by selection effects. The metal-rich population in the solar neighbourhood is composed of relatively old and cool stars that have already undergone some Li depletion; hence, their measured Li does not represent the initial interstellar medium abundance, but a lower limit to it.