Catalyzes the desulfonation and deamination of L-cysteate, yielding pyruvate, sulphite and ammonium. Involved in sulfolactate degradation. H2O + L-cysteate = H(+) + NH4(+) + pyruvate + sulfite Induced during growth on sulfolactate or cysteate. Belongs to the ACC deaminase/D-cysteine desulfhydrase family.