Catalyzes the transformation of cystathionine to homocysteine. Can also use cystine or S-methylcysteine as substrate. H2O + L,L-cystathionine = L-homocysteine + NH4(+) + pyruvate an S-substituted L-cysteine + H2O = a thiol + NH4(+) + pyruvate Activity increases by approximately two-fold in the presence of GCBP. Interacts with GCBP (TTHA1554). Belongs to the class-II pyridoxal-phosphate-dependent aminotransferase family. MalY/PatB cystathionine beta-lyase subfamily.