Crystallographic orientation analysis revealed that DyNi2 grew epitaxially on Ni, whereas NdNi2 does not. To elucidate the microscopic origin of this contrasting behavior, we constructed atomistic models of Ni/Rare-earth (RE)Ni2 interfaces with well-defined crystallographic alignment and performed first-principles calculations based on density functional theory (DFT). The computed interfacial energies exhibit a clear correlation with lattice mismatch: larger mismatch leads to higher interfacial energy and reduced interface stability. Consequently, Ni/DyNi2 exhibits a significantly lower interfacial energy than Ni/NdNi2, consistent with experimental observations. A comparison between interfacial and strain energies for Ni/RENi2 (RE = Sc, Y, Nd, Gd, Dy, and Lu) reveals that the elemental dependence of interfacial stability is dominated by elastic strain rather than chemical bonding. Based on this insight, we developed a simple regression model using the absolute lattice mismatch as a descriptor, enabling qualitative predictions of stability for Ni/RENi2 interfaces with RE other than those examined in DFT.