Improving the catalytic performance of materials based on cerium oxide (CeO2) for the activation of methane (CH4) can be achieved through the following strategies: mixture of CeO2 with different oxides (e.g., CeO2-La2O3) and the use of particles with different sizes. In this study, we present a theoretical investigation of the initial CH4 dehydrogenation on (La2Ce2O7)n clusters, where n = 2, 4, and 6. Our framework relies on density functional theory calculations combined with the unity bond index-quadratic exponential potential approximation. Our results indicate that chemical species arising from the first dehydrogenation of CH4, that is, CH3 and H, bind through the formation of C-O and H-O bonds with the clusters, respectively. The coordination of the adsorption site and the chemical environment plays a crucial role in the magnitude of the adsorption energy; for example, species adsorb more strongly in the low-coordinated topO sites located close to the La atoms. Thus, it affects the activation energy barrier, which tends to be lower in configurations where the adsorption of the chemical species is stronger. During CH4 dehydrogenation, the CH3 radical can be present in a planar or tetrahedral configuration. Its conformation changes as a function of the charge transference between the molecule and the cluster, which depends on the CH3-cluster distance. Finally, we analyze the effects of the Hubbard effective parameter (Ueff) on adsorption properties, as the magnitude of localization of Ce f-states affects the hybridization of the interaction between the molecule and the clusters and hence the magnitude of the adsorption energies. We obtained a linear decrease in the adsorption energies by increasing the Ueff parameter; however, the activation energy is only slightly affected.