This work aims to investigate the behaviour of the lithium abundance in stars with and without detected planets. Our study is based on a sample of 1332 FGK main-sequence stars with measured lithium abundances, for 257 of which planets were detected. Our method reviews the sample statistics and is addressed specifically to the influence of tides and orbital decay, with special attention to planets on close orbits, whose stellar rotational velocity is higher than the orbital period of the planet. In this case, tidal effects are much more pronounced. The analysis also covers the orbital decay on a short timescale, with planets spiralling into their parent star. Furthermore, the sample allows us to study the relation between the presence of planets and the physical properties of their host stars, such as the chromospheric activity, metallicity, and lithium abundance. In the case of a strong tidal influence, we cannot infer from any of the studies described that the behaviour of Li differs between stars that host planets and those that do not. Our sample includes stars with super-solar metallicity ([Fe/H]>0.15dex) and a low lithium abundance (A(Li)<1.0dex). This enabled us to analyse scenarios of the origin and existence of these stars. Considering the possible explanation of the F dip, we show that it is not a plausible scenario. Our analysis is based on a kinematic study and concludes that the possible time that elapsed in the travel from their birth places in the central regions of the Galaxy to their current positions in the solar neighbourhood is not enough to explain the high lithium depletion. It is remarkable that those of our high-metallicity low-lithium stars with the greatest eccentricity (e>0.2) are closest to the Galactic centre. A dedicated study of a set of high-metallicity low-Li stars is needed to test the migration-depletion scenario.