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We exploit the unique characteristics of a sample of open clusters (OCs) and field stars for which high-precision 7Li abundances and stellar parameters are homogeneously derived by the Gaia-ESO Survey (GES). We derive possibly undepleted 7Li abundances for 26 OCs and star forming regions with ages from young to old spanning a large range of Galactocentric distances, which allows us to reconstruct the local late Galactic evolution of lithium as well as its current abundance gradient along the disc. Field stars are added to look further back in time and to constrain 7Li evolution in other Galactic components. The data are then compared to theoretical tracks from chemical evolution models that implement different 7Li forges. We find that the upper envelope of the 7Li abundances measured in field stars of nearly solar metallicities traces very well the level of lithium enrichment attained by the ISM as inferred from observations of cluster stars. We confirm previous findings that the abundance of 7Li in the solar neighbourhood does not decrease at supersolar metallicity. The comparison of the data with the chemical evolution model predictions favours a scenario in which the majority of the 7Li abundance in meteorites comes from novae. Current data also seem to suggest that the nova rate flattens out at later times. This requirement might have implications for the masses of the white dwarf nova progenitors and deserves further investigation. Neutrino-induced reactions taking place in core-collapse supernovae also produce some fresh lithium. This likely makes a negligible contribution to the meteoritic abundance, but could be responsible for a mild increase of the 7Li abundance in the ISM of low-metallicity systems that would counterbalance the astration processes., 17 pages, 10 figures, 3 tables (full tables 1 and 3 only available at the CDS), accepted for publication in Astronomy and Astrophysics. Version 2 includes corrections from language editor