Despite the recent availability of large samples of stars with high-precision Li abundances , there are many unanswered questions about the evolution of this unique element in the Galaxy and in the stars themselves . It is unclear which parameters and physical mechanisms that govern Li depletion in late-type stars and if Galactic enrichment has proceeded differently in different stellar populations . With this study we aim to explore these questions further by mapping the evolution of Li with stellar mass , age , and effective temperature for Milky Way disk stars , linking the metal-poor and metal-rich regimes , and how Li differs in the thin and thick disks . We determine Li abundances for a well-studied sample of 714 F and G dwarf , turn-off , and subgiant stars in the solar neighbourhood . The analysis is based on line synthesis of the ^ { 7 } Li line at 6707 Å in high-resolution and high signal-to-noise ratio echelle spectra , obtained with the MIKE , FEROS , SOFIN , UVES , and FIES spectrographs . The presented Li abundances are corrected for non-LTE effects . Out of the sample of 714 stars we are able to determine Li abundances for 420 stars and upper limits on the Li abundance for another 121 stars . 36 stars are listed as exoplanet host stars , and 18 of those have well-determined Li abundances and 6 have Li upper limits . Our main finding is that there are no signatures of Li production in stars associated with the thick disk . Instead the Li abundance trend is decreasing with metallicity for these thick disk stars . Significant Li production is however seen in the thin disk , with a steady increase towards super-solar metallicities . At the highest metallicities , however , around [ Fe / H ] \approx + 0.3 , we tentatively confirm the recent discovery that the Li abundances level out . Our finding contradicts the other recent studies that found that Li is also produced in the thick disk . We find that this is likely due to the \alpha -enhancement criteria those studies used to define their thick disk samples . By using the more robust age criteria we are able to define a thick disk stellar sample that is much less contaminated by thin disk stars . Furthermore , we also tentatively confirm the age-Li correlation for solar twin stars , and we find that there is no correlation between Li abundance and whether the stars have detected exoplanets or not . The major conclusion that can be drawn from this study is that no significant Li production , relative to the primordial abundance , took place during the first few billion years of the Milky Way , an era coinciding with the formation and evolution of the thick disk . Significant Li enrichment then took place once long-lived low-mass stars ( acting on a time-scale longer than SNIa ) have had time to contribute to the chemical enrichment of the interstellar medium .