We aim, on the one hand, to study the possible differences of Li abundances between planet hosts and stars without detected planets at effective temperatures hotter than the Sun, and on the other hand, to explore the Li dip and the evolution of Li at high metallicities. We present lithium abundances for 353 main sequence stars with and without planets in the T_eff_ range 5900-7200K. We observed 265 stars of our sample with HARPS spectrograph during different planets search programs. We observed the remaining targets with a variety of high-resolution spectrographs. The abundances are derived by a standard local thermodynamic equilibrium analysis using spectral synthesis with the code MOOG and a grid of Kurucz ATLAS9 atmospheres. We find that hot jupiter host stars within the T_eff_ range 5900-6300K show lower Li abundances, by 0.14dex, than stars without detected planets. This offset has a significance at the level 7{sigma}, pointing to a stronger effect of planet formation on Li abundances when the planets are more massive and migrate close to the star. However, we also find that the average vsini of (a fraction of) stars with hot jupiters is higher on average than for single stars in the same T_eff_ region, suggesting that rotational-induced mixing (and not the presence of planets) might be the cause for a greater depletion of Li. We confirm that the mass-metallicity dependence of the Li dip is extended towards [Fe/H]~0.4dex (beginning at [Fe/H]~-0.4dex for our stars) and that probably reflects the mass-metallicity correlation of stars of the same T_eff_ on the main sequence. We find that for the youngest stars (<1.5Gyr) around the Li dip, the depletion of Li increases with vsini values, as proposed by rotationally-induced depletion models. This suggests that the Li dip consists of fast rotators at young ages whereas the most Li-depleted old stars show lower rotation rates (probably caused by the spin-down during their long lifes). We have also explored the Li evolution with [Fe/H] taking advantage of the metal-rich stars included in our sample. We find that Li abundance reaches its maximum around solar metallicity, but decreases in the most metal-rich stars, as predicted by some models of Li Galactic production.