Many theoretical studies address the interaction of different atoms with graphene; however, the relevant information on the adsorption of the lanthanide species remains limited and controversial, creating a gap in this important area of graphene chemistry and physics. By employing periodic density functional theory calculations, we provide the key theoretical information for the entire series from lanthanum to lutetium interacting with defect-free graphene, including the interaction strength and distances, charge and spin of the lanthanide atoms, and comparative features of the density of states. The central lanthanides Gd, Tb, and Dy exhibit the strongest bonding and shortest distances. The positive charge acquired by the lanthanide atoms varies insignificantly, with the exception of Yb and Lu with a filled 4f shell. The spin increases from La to Tb and then decreases sharply, achieving minimal values for Tm, Yb, and Lu. Interaction with graphene influences even the deeper 5s and 5p shells.