Catalyzes the epimerization of L-Ile-L-Tyr to L-Ile-D-Tyr (in vitro). Catalyzes the epimerization of dipeptides, with a preference for substrates with a hydrophobic or basic amino acid in the first position, followed by an aromatic residue in the second position. Has epimerase activity with L-Ile-L-Tyr, L-Val-L-Tyr and L-Arg-L-Tyr (in vitro). Binds 1 Mg(2+) ion per subunit. kcat is 9.2 sec(-1) for epimerization of L-Ile-L-Tyr. kcat is 8.7 sec(-1) for epimerization of L-Val-L-Tyr. kcat is 15 sec(-1) for epimerization of L-Arg-L-Tyr. Part of a large, functionally divergent protein family. Protein modeling and substrate docking was used to predict the substrate specificity, prior to biochemical analysis. Belongs to the mandelate racemase/muconate lactonizing enzyme family.