By using DFT calculations, we addressed the influence of topological defects on the bonding strength and some electronic parameters for lanthanide atoms La0 and Lu0, ions La3+ and Lu3+ interacting with graphene. The results obtained for the cluster models containing isolated pentagon (5), Stone-Wales (SW) defect and pyracylene unit (5665), as well as for C60 fullerene, were compared to those for a defect-free graphene model (G). We found that topological defects are always preferential sites for Lnn adsorption, as compared to pristine graphene. Particular orders of complex stability depend on lanthanide species, carbon cluster model, the Lnn position when the cluster has positive curvature (‘endo’, inside, or ‘exo’, outside), and are as follows: for La0, 5665_endo > SW > 5_endo > 5_exo > 5665_exo > C60 > G; for La3+, SW > G > 5665_endo > 5665_exo > 5_endo > 5_exo > C60; for Lu0, 5665_endo > 5_endo > 5_exo > SW > 5665_exo > C60 > G; for Lu3+, SW > G > 5665_endo > 5_endo > 5665_exo > 5_exo > C60. Ln…C distances, frontier orbital energies, HOMO, LUMO and spin density plots, as well as charge and spin on Lnn species from Mulliken population analysis are presented.