The complexes formed by the singly-charged S-state lanthanide ions Eu+, Yb+ and Lu+ with the hydrogen molecule are investigated using the ab initio coupled cluster CCSD(T) method with effective core potential and all-electron descriptions of lanthanides. Equilibrium structures, two-dimensional interaction potential energy surfaces and variational energies of the lowest rovibrational energy levels are obtained. Three complexes considered are qualitatively similar and exhibit weak bonding and perturbation of hydrogen fragment, as well as strong vibrational anharmonicity.