Context. Open clusters provide unambiguous clues to understand the evolution of 7 Li at the surface of low-mass stars and its possible correlation with stellar rotation, which is a challenge for both stellar hydrodynamics and Galactic chemical evolution. Aims. We aim to quantify the efficiency of the transport processes for both angular momentum and chemicals that are required to explain simultaneously the observed behaviour of surface 7 Li (and 9 Be) and rotation as well as the internal rotation profiles inferred from helio- and asteroseismology in F- and G-type main sequence stars. Methods. We apply the model for the transport of angular momentum and chemicals that we tailored in a previous work for solar-type stars to an extended range of initial masses and metallicities corresponding to F- an G-type stars in a sample of 20 Galactic open clusters. We evaluate its ability to explain the 7 Li, 9 Be, and rotation periods observations. This model includes atomic diffusion, rotation-induced processes (for which we tested different prescriptions for shear turbulence), penetrative convection with a rotational dependence, parametric viscosity and turbulence, and magnetic braking. Results. Over the entire range of masses, metallicities, and ages explored, we reproduce the evolution of the surface rotation rates and predict, for the first time, the observed anti-correlation between the surface rotation rate and 7 Li depletion as a consequence of the penetrative convection prescription. The 7 Li behaviour and its evolution with time is well reproduced for G-type stars. However, the ability of the model to reproduce the so-called 7 Li dip centred around ∼6600 K strongly depends on the adopted prescriptions for shear turbulence. It also requires a stellar mass dependence for the parametric viscosity adopted for the transport of angular momentum, similar to the behaviour predicted for the generation and luminosity of internal gravity waves generated by stellar convective envelopes. Finally, the model predicts internal rotation profiles in good agreement with asteroseismic constraints in main sequence stars. Conclusions. We provide an efficient way to model G-type stars of different ages and metallicities successfully. However, the 7 Li and 9 Be dip constraints urgently call for further hydrodynamical studies to better model turbulence in stars, and for the exploration of physical processes such as tachocline mixing for the transport of chemicals and internal gravity waves for the transport of angular momentum. Finally, additional data for the internal rotation and for 9 Be in main sequence low-mass stars are definitively needed.