Catalyzes the conversion of hemimercaptal, formed from methylglyoxal and glutathione, to S-lactoylglutathione. (R)-S-lactoylglutathione = glutathione + methylglyoxal Binds 1 zinc ion per subunit. Secondary metabolite metabolism; methylglyoxal degradation; (R)-lactate from methylglyoxal: step 1/2. A number of isoforms are produced. According to EST sequences. Belongs to the glyoxalase I family.