Catalyzes the conversion of hemimercaptal, formed from methylglyoxal and glutathione, to S-lactoylglutathione. Active toward the hemithioacetal adducts formed by reacting methylglyoxal or phenylglyoxal with glutathione, homoglutathione or gamma-glutamylcysteine, showing no preference for homoglutathione adducts over glutathione adducts. (R)-S-lactoylglutathione = glutathione + methylglyoxal Binds 3 zinc ions per subunit, but unlike the enzyme from mammals, shows full activity in the absence of metal ions. Secondary metabolite metabolism; methylglyoxal degradation; (R)-lactate from methylglyoxal: step 1/2. Homodimer. Zinc ions may be required for the correct assembly of the enzyme but are not required for catalysis. Belongs to the glyoxalase I family.