The interfaces between liquid or solid Pb islands and single-or poly-crystalline Cu substrates are investigated. EBSD (Electron backscattered diffraction) analyses show that when Pb is solidified from droplets, a cube-on-cube orientation relationship prevails between the Pb crystals and each Cu grain surface, whatever its surface orientation, even though the lattice parameter of Pb is 1.37 times larger than that of Cu. Scanning electron microscope (SEM) and atomic force microscope (AFM) analyses show that during annealing of Pb droplets, ridges develop at the droplet-substrate triple lines, indicating that the interfaces evolve towards equilibrium by diffusional processes. These features are discussed in comparison with experiments and calculations performed on Pb nanocrystals embedded in Al, another fcc solid with a lattice parameter smaller than that of Pb. It is proposed that the cube-on-cube orientation relationship results from the solidification of Pb along the {111} planes of the solid Cu/liquid Pb interface which have developed by diffusion during the process of equilibration of the interface shape.