Catalyzes the conversion of hemimercaptal, formed from methylglyoxal and glutathione, to S-lactoylglutathione. (R)-S-lactoylglutathione = glutathione + methylglyoxal Binds 1 zinc ion per subunit. Cobalt, nickel and manganese ions can also function as cofactors. Optimum pH is 5.5-7.5. Secondary metabolite metabolism; methylglyoxal degradation; (R)-lactate from methylglyoxal: step 1/2. Monomer. Belongs to the glyoxalase I family.