Degenerate four-wave mixing signals excited by femtosecond laser pulses were measured in LaCuOCh (Ch = S and Se) at 4 K. The signals for LaCuOS exhibit a beat structure with a period of 480 fs just at the exciton peak energy, indicating that the lowest exciton states are split by 9 meV, but no beat structure was observed in LaCuOSe, regardless of the laser's energy. The spin--orbit interaction of the Ch ion accompanied by the hybridization of Cu 3d orbitals causes splitting of the exciton levels. Furthermore, the contribution of Ch p orbitals in the valence band maximum is larger in LaCuOSe owing to increased covalency in the Cu--Ch bond when S is replaced with Se.