Recent detection of the isotope $^7$Be (that decays into $^7$Li) in the outburst of classical novae confirms the suggestion made in the 70s that novae could make $^7$Li. We reconsidered the role of novae as producers of Li by means of a detailed model of the chemical evolution of the Milky Way. We showed that novae could be the Galactic lithium source accounting for the observed increase of Li abundances in the thin disk with stellar metallicity. The best agreement with the upper envelope of the observed Li abundances is obtained for a delay time of ~ 1 Gyr for the nova production and for an effective Li yield of $1.8 (\pm 0.6) \times 10^{-5}$ $M_{\odot}$ over the whole nova life. Lithium in halo stars is depleted by ~ 0.35 dex, assuming the pristine abundance from standard big bang nucleosynthesis. We elaborate a model that matches the pristine stellar abundances, assuming that all stars are depleted by 0.35 dex. In this case, the delay remains the same, but the Li yields are doubled compared to the previous case. This model also has the merit to match the Li abundance in meteorites and young TTauri stars. The thick disk model, adopting the parameters derived for the thin disk, can also explain the absence of increase of Li abundances in its stars. The thick disk is old, but formed and evolved in a time shorter than that required by novae to contribute significantly to Li. Therefore, no Li enhancement is expected in thick disk stars. We show that the almost constant Li abundance in the thick disk results from the compensation of stellar astration by spallation processes.

13 pages, 7 figures, accepted for publication in MNRAS