Catalyzes the cleavage of cystathionine to homocysteine, pyruvate and ammonia during methionine biosynthesis. H2O + L,L-cystathionine = L-homocysteine + NH4(+) + pyruvate an S-substituted L-cysteine + H2O = a thiol + NH4(+) + pyruvate Amino-acid biosynthesis; L-methionine biosynthesis via de novo pathway; L-homocysteine from L-cystathionine: step 1/1. Belongs to the trans-sulfuration enzymes family.