Catalyzes the conversion of cystathionine to cysteine, and homocysteine to sulfide. H2O + L,L-cystathionine = 2-oxobutanoate + L-cysteine + NH4(+) H2O + L-homocysteine = 2-oxobutanoate + H(+) + hydrogen sulfide + NH4(+) By methionine. Repressed by sulfate and cysteine. No visible phenotype. Belongs to the trans-sulfuration enzymes family.