Probing the origins. II. Unravelling lithium depletion and stellar motion: Intrinsic stellar properties drive depletion, not kinematics

Context. Lithium (Li) is a complex yet fragile element, with many production pathways but is easily destroyed in stars. Previous studies observe that the top envelope of the distribution of Li abundances A(Li) in super-solar metallicity dwarf stars shows signs of Li depletion, contrary to expectations. This depletion is thought to result from the interplay between stellar evolution and radial migration. Aims. In Paper I, we classified a stellar sample from the thin disc with a broad range in metallicity as being churned outwards or inwards, or as stars where angular momentum was preserved (a category including blurred and undisturbed stars, which our method does not separate). In this paper (Paper II), we delve deeper by analysing our entire metallicity-stratified sample along with their dynamic properties, focusing on the connection between radial migration and Li depletion. Methods. We analysed the chemo-dynamics of a set of 1188 thin-disc dwarf stars observed by the Gaia-ESO survey, previously classified into six metallicity-stratified groups via hierarchical clustering (HC), ranging from metal-poor to super-metal-rich. We examined several features, such as effective temperatures, masses, and dynamic properties. We also implemented a parametric survival analysis using penalised splines (logistic distribution) to quantify how stellar properties and motion (or migration) direction jointly influence Li depletion patterns. Results. Stars in our sample that seemingly churned outwards are predominantly Li-depleted, regardless of their metallicities. These stars are also the oldest, coldest, and least massive compared to those in the same HC group that either churned inwards or kept their orbital radii. Our survival analysis confirms temperature as the primary driver of Li depletion, followed by metallicity and age, while migration direction shows negligible influence. Additionally, the proportion of outward-churned stars increases with increasing metallicity, making up more than 90% of our sample in the most metal-rich group. Conclusions. The increasing proportion of outward-churned stars with higher metallicity (and older ages) indicates their dominant influence on the overall trend observed in the [Fe/H]-A(Li) space for stellar groups with [Fe/H]>0. The survival model reinforces the finding that the observed Li depletion stems primarily from intrinsic stellar properties (cool temperatures, higher metallicity, and old ages) rather than migration history. This suggests the metallicity-dependent depletion pattern emerges through stellar evolution rather than Galactic dynamical processes.