  Unraveling the cosmological Li problem - the discrepancy between Big Bang
nucleosynthesis predictions and observed values in the Spite plateau - requires
a comprehensive exploration of stellar evolution. In this study, we utilized
the code STAREVOL to compute the stellar evolution models with atomic
diffusion, rotation-induced processes, parametric turbulence, and additional
viscosity. We calibrated the models to fit the abundance of Li in Population II
stars selected from the GALAH DR3 spectroscopic survey and literature
compilation based on their chemical composition. The calibration reveals the
significance of parametric turbulence in counteracting atomic diffusion
effects. These models predict the constancy of the Spite plateau as a function
of $T_\mathrm{eff}$ and [Fe/H] which agrees with the observational trend found
after a detailed selection of dwarf non-peculiar stars. Other dwarfs that lie
below the Spite plateau are either CEMP or have other types of chemical
peculiarities, reinforcing the notion of their environmental origin. The Li
abundance near the Spite plateau of the most Fe-deficient star, J0023+0307,
which is not CEMP, provides additional evidence for the stellar depletion
solution of the Li cosmological problem. Also, our models predict a transition
from Li constancy at low metallicities to dispersion at high metallicities
which is seen in observations. In addition, we extend our analysis to include a
comparison with observational data from the globular cluster NGC 6752,
showcasing excellent agreement between model predictions and Li and Mg trends
in post-turnoff stars. This opens avenues for refining the estimates of initial
Li abundance in metal-rich globular clusters which would help to constrain Li
evolution in the Milky Way.
