The chemical evolution of lithium in the Milky Way represents a major problem in modern astrophysics. Indeed, lithium is, on the one hand, easily destroyed in stellar interiors, and, on the other hand, produced at some specific stellar evolutionary stages that are still not well constrained. The goal of this paper is to investigate the lithium stellar content of Milky Way stars in order to put constraints on the lithium chemical enrichment in our Galaxy, in particular in both the thin and thick discs. Thanks to high-resolution spectra from the ESO archive and high quality atmospheric parameters, we were able to build a massive and homogeneous catalogue of lithium abundances for 7300 stars derived with an automatic method coupling, a synthetic spectra grid, and a Gauss-Newton algorithm. We validated these lithium abundances with literature values, including those of the Gaia benchmark stars. In terms of lithium galactic evolution, we show that the interstellar lithium abundance increases with metallicity by 1 dex from [M/H]=-1 dex to +0.0 dex. Moreover, we find that this lithium ISM abundance decreases by about 0.5 dex at super-solar metalllicity. Based on a chemical separation, we also observed that the stellar lithium content in the thick disc increases rather slightly with metallicity, while the thin disc shows a steeper increase. The lithium abundance distribution of alpha-rich, metal-rich stars has a peak at A(Li)~3 dex. We conclude that the thick disc stars suffered of a low lithium chemical enrichment, showing lithium abundances rather close to the Spite plateau while the thin disc stars clearly show an increasing lithium chemical enrichment with the metallicity, probably thanks to the contribution of low-mass stars.

15 pages, 12 figures, 2 tables