Catalyzes the epimerization of L-Ala-D-Glu to L-Ala-L-Glu and has a role in the recycling of the murein peptide, of which L-Ala-D-Glu is a component. Is also able to catalyze the reverse reaction and the epimerization of all the L-Ala-X dipeptides, except L-Ala-L-Arg, L-Ala-L-Lys and L-Ala-L-Pro. Is also active with L-Gly-L-Glu, L-Phe-L-Glu, and L-Ser-L-Glu, but not with L-Glu-L-Glu, L-Lys-L-Glu, L-Pro-L-Glu, L-Lys-L-Ala, or D-Ala-D-Ala. L-alanyl-L-glutamate = L-alanyl-D-glutamate Binds 1 Mg(2+) ion per subunit. Cell wall biogenesis; peptidoglycan recycling. Monomer. Belongs to the mandelate racemase/muconate lactonizing enzyme family. Truncated C-terminus.