Fission products, including rare earth elements, are incorporated into the fuel matrix through the operational life of the fuel in a nuclear reactor, at the same time the chemistry of uranium evolves to higher oxidation states with burn up. This evolution results in the formation of complex (multicomponent) oxides that are encompassed within the ternary oxide system UO2-UO3-Ln2O3 (where Ln stand for a lanthanide). We investigate the crystallographic and electronic structure of Ln-U-O compounds that may be formed inside nuclear fuel operational life using density functional theory (DFT) calculations. We used a layered atomic model to propose ordered structures and compared their stability to disordered phases. We also employed the atom-in-molecule (AIM) approach to study the oxidation state of uranium atoms and the iconicity/covalency of the U-O bonds. The AIM analyses revealed a quantitative inverse correlation between the charge density at the bonding critical points and the U-O bond length.