Catalyzes the conversion of hemimercaptal, formed from methylglyoxal and glutathione, to S-lactoylglutathione (PubMed:8719777). Involved in the regulation of TNF-induced transcriptional activity of NF-kappa-B (By similarity). Required for normal osteoclastogenesis (By similarity). (R)-S-lactoylglutathione = glutathione + methylglyoxal Binds 1 zinc ion per subunit. In the homodimer, two zinc ions are bound between subunits. Secondary metabolite metabolism; methylglyoxal degradation; (R)-lactate from methylglyoxal: step 1/2. Homodimer. Glutathionylation at Cys-139 inhibits enzyme activity. Phosphorylated at Thr-107 in the presence of CaMK2. However, this is a consensus site for phosphorylation by CK2 so phosphorylation may be mediated by CK2 rather than CaMK2. Phosphorylation is induced by TNF and suppresses the TNF-induced transcriptional activity of NF-kappa-B (By similarity). Exists in a nitric oxide (NO)-modified form. The exact nature of the modification is unknown, but it suppresses the TNF-induced transcriptional activity of NF-kappa-B (By similarity). Belongs to the glyoxalase I family.