The present work is focused on nickel catalysts supported on La₂O₃-CeO₂ binary oxides without and with the addition of Cu to the active component for the dry reforming of methane (DRM). The catalysts are characterized using XRD, XRF, TPD-CO₂, TPR-H₂, and low-temperature N₂ adsorption–desorption methods. This work shows the effect of different La:Ce ratios (1:1 and 9:1) and the Cu addition on the structural, acid base, and catalytic properties of Ni-containing systems. The binary LaCeO_x oxide at a ratio of La:Ce = 1:1 is characterized by the formation of a solid solution with a fluorite structure, which is preserved upon the introduction of mono- or bimetallic particles. At La:Ce = 9:1, La₂O₃ segregation from the solid solution structure is observed, and the La excess determines the nature of the precursor of the active component, i.e., lanthanum nickelate. The catalysts based on LaCeO_x (1:1) are prone to carbonization during 6 h spent on-stream with the formation of carbon nanotubes. The Cu addition facilitates the reduction of the Cu-Ni catalyst carbonization and increases the number of structural defects in the carbon deposition products. The lanthanum-enriched LaCeO_x (9:1) support prevents the accumulation of carbon deposition products on the surface of CuNi/La₂O₃-CeO₂ 9:1, providing high DRM activity and an H₂/CO ratio of 0.9.