Herein, we studied the structure and hydrogenation of graphene supported on hydrogen-terminated SiC, with intercalated Li atoms. Strong nonbonded interactions occur between graphene and the Si-H groups. The latter were found to be significantly augmented by the intercalation of Li atoms, which enhanced the SiH::pi interactions. Although the electronic structure of graphene did not experience significant changes when supported on hydrogen-terminated SiC, a small gap of 0.04 eV was computed at the HSEH1PBE/6-31G* level. The clustering of Li atoms over graphene was prevented by the SiC support. A significant enhancement of reactivity could be corroborated due to the presence of intercalated Li atoms, given that the C-H binding energy was increased by almost 1 eV with respect to pristine graphene. We expect that hydrogen-terminated SiC with intercalated Li atoms can be used to enhance the chemical reactivity of graphene, given that it strongly interacts with graphene but does not compete for the electrons donated by Li.