Numerous applications of graphene involve quasi-infinite sheets, as well as finite structures with edges, pores, graphene quantum dots, etc. In theoretical studies of adsorption of diverse chemical species, including single atoms, molecules, cations, and anions, graphene usually behaves as a very rigid planar structure. However, we found that when adsorbing lanthanide atoms, finite size structures, represented by the widely used supercoronene model, can undergo considerable distortion, and the degree of distortion depends on the number of unpaired electrons, reaching a maximum for Gd (eight unpaired electrons). Lanthanides closely approach the supercoronene surface and increase the interaction energy. Extrapolating to real-world systems, one can expect the existence and magnitude of lanthanide-induced distortion to depend on the size of graphene structures. Quasi-infinite or very large graphene sheets are too rigid to undergo such bending, but it becomes tangible for graphene quantum dots and for atom adsorption closer to graphene edges.