Realizing hybrids of low-dimensional Kondo lattices and superconducting substrates leads to fascinating platforms for studying the exciting physics of strongly correlated electron systems with induced superconducting pairing. Here, we report a scanning tunneling microscopy and spectroscopy study of a new type of two-dimensional (2D) La–Ce alloy grown epitaxially on a superconducting Re(0001) substrate. We observe the characteristic spectroscopic signature of a hybridization gap evidencing the coherent spin screening in the 2D Kondo lattice realized by the ultrathin La–Ce alloy film on normal conducting Re(0001). Upon lowering the temperature below the critical temperature of rhenium, a superconducting gap is induced exhibiting an energy asymmetry of the coherence peaks that arises from the interaction of residual unscreened magnetic moments with the superconducting substrate. A positive correlation between the Kondo hybridization gap and the asymmetry of the coherence peaks is found.