Catalyzes the epimerization of dipeptides with L-Glu in the second position. Has epimerase activity with L-Ala-L-Glu, L-Pro-L-Glu, L-Val-L-Glu, L-Thr-L-Glu and L-Met-L-Glu (in vitro). Binds 1 Mg(2+) ion per subunit. 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.