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The lithium present in the photospheres of solar-type stars is transported to the inner parts by convection, reaching regions even somewhat below the convection zone, by non-standard transport mechanisms. In stars with deeper convective zones, this element can reach regions with temperatures sufficient enough to be destroyed, implying in a lower Li content. More metallic stars show a deepening of their convective zones, so they could deplete more Li in comparison with stars of lower metallicity. In order to verify this effect and its amplitude, we selected stars with ~1 M$_{\odot}$ and metallicities within a factor of two relative to the Sun. We studied a sample of 41 metal-rich and -poor solar analogues, and carried out a joint analysis with a sample of 77 solar twins from our previous work, resulting in a total sample of 118 stars covering the metallicity range -0.3 $\leq$ [Fe/H] $\leq$ +0.3 dex. We employed high-resolution (R = 115 000) and high-signal-to-noise ratio (S/N = 400-1000) HARPS spectra and determined the atmospheric parameters using a line-by-line differential analysis and the Li abundance through spectral synthesis. The ages and masses of the whole sample were improved by refining the isochronal method. We also investigated the impact of planets on Li. We found robust anticorrelations between Li abundance and both metallicity and age, with a significance above 10$\sigma$ in both cases. Our results agree qualitatively with theoretical predictions and are useful to constrain non-standard models of Li depletion, and to better understand transport and mixing mechanisms inside stars., Comment: 10 pages, 5 figures, 2 tables