Robust modelling of solar-like stars is key to understanding the evolution of low-mass stars and understand their environment. So far, no clear consensus appears for which physics is required to reproduce the main observables: the evolution of light elements (e.g. lithium), the evolution of surface rotation with time as observed in open clusters, and the state of the internal rotation obtained with the help of asteroseismology. In order to improve stellar modelling and prepare the PLATO space mission, we need to understand these observations and better characterise internal transport processes in stars. Using the stellar evolution code STAREVOL, we compute the lithium abundance as well as the surface and internal rotation evolutions from models of main-sequence rotating stars that include atomic diffusion and additional transport for both chemicals and angular momentum. We test for the first time mixing processes including a rotation-dependent penetrative convection (Augustson et al. 2019). We then compare the results to observations of G-type and F-type stars. We succeed to reproduce the observational constraints at different masses and metallicities during evolution. We discuss the relevance and the efficiency of these different additional transport processes. We show that for the specific case of the Li-dip for F-type stars, we need to involve a stronger shear-turbulence and an additional transport process of angular momentum consistent with internal gravity waves (Dumont et al. 2021a and 2021b).