The lack of description of van der Waals interactions in layered materials such as graphite and binary graphite intercalation compounds remains a main drawback of conventional density functional theory. Two fundamentally different approaches to overcome this issue are the employment of semiempirical dispersion correction scheme such as Grimme dispersion correction or nonlocal density functionals. We carefully compare these two approaches for the description of the geometric structure and the thermodynamic stability of pure graphite and Li-GICs at different lithium concentrations and stages. Based on the computed formation energies, we also evaluate the lithium-graphite intercalation potential. We find that PBE-D3(BJ) accurately reproduces the lattice parameters and the interlayer binding energy of graphite, although it underestimates the thermodynamic stability of stage-II Li-GICs mainly due to overbinding of carbon atoms in pure graphite. The nonlocal van der Waals functionals optB88-vdW, optB86b-vdW, and revPBE-vdW show a good agreement with experiments concerning stability of Li-GICs of different stages, although they overestimate the van der Waals interactions in graphite. The experimentally determined decreasing step-function behavior of Li-graphite intercalation potential can be qualitatively reproduced only by employing the revPBE van der Waals functional, whereas the other density functionals fail in the description.