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.