We have performed a theoretical analysis of the recently reported photoelectron (PE) spectra of the series of sandwich complex anions Ln(COT)(2)(-) (Ln = La-Lu, COT = 1,3,5,7-cyclooctatetraene), focusing on the Ln dependence of the vertical detachment energies. For most Ln, the pi molecular orbitals, largely localized on the COT ligands, have the energy order of e(1g) < e(1u) < e(2g) < e(2u), as in the actinide analogues, reflecting the substantial orbital interaction with the Ln 5d and 5p orbitals. Thus, it would be expected that the lanthanide contraction would increase the orbital interaction so that the overlaps between the COT pi and Ln atomic orbitals tend to increase across the series. However, the PE spectra and theoretical calculations were not consistent with this expectation, and the details have been clarified in this study. Furthermore, the energy level splitting patterns of the anion and neutral complexes have been studied by multireference ab initio methods, and the X peak splittings observed in the PE spectra only for the middle-range Ln complexes were found to be due to the specific interaction between the Ln 4f and ligand pi orbitals of the neutral complexes in e(2u) symmetry. Because the magnitude of this 4f-ligand interaction depends critically on the final state 4f electron configuration and the spin state, a significant Ln dependence in the PE spectra is explained.