Compounds belonging to the La-U-O phase space are of technological interest in light water nuclear reactor fuel technology. Mixed uranium-lanthanide oxide compounds form in the UO2 fuel pellets as lanthanides fission products are incorporated into the fuel during burn-up. Also, lanthanide burnable nuclear poisons (especially Gd) can be added on purpose to urania to control the excess of reactivity in enriched fuels. We believe that different annealing conditions may actually help controlling the distribution of lanthanides in the fluorite derived structures, producing local compositional fluctuations that may significantly deviate from the average random picture. The existence of short or intermediate range order (correlations) can be assessed by diffraction using TEM and X-rays. We have used experiments and simulation to determine the structures of this family of compounds. Diffuse or sharp superstructures along [111]c observed for some compositions suggest that these compounds can be modeled using alternating layers normal to that direction. In this model, the unit cell is composed of alternating planes of anions and cations, which allows us to study in-plane cation ordering. Starting with the parent fluorite phase, and the information either available from existing experimental results or by systematic exploration of the possible solutions involving small supercells, we have determined the symmetry-compatible ordered atomic arrangements of these family of compounds. Density functional theory allows to determine the lowest energy configurations of cations among these layered atom models. Using wet chemistry we have actually synthesized those samples with the most interesting compositions predicted by the numerical modelling, and characterized them by x-ray diffraction and transmission electron microscopy to assess the predictions.