Catalyzes the reversible epimerization of cellobiose to 4-O-beta-D-glucopyranosyl-D-mannose (Glc-Man). Can also epimerize cellotriose to Glc-Glc-Man, cellotetraose to Glc-Glc-Glc-Man, and lactose to epilactose. D-cellobiose = beta-D-glucosyl-(1->4)-D-mannopyranose Enhanced by Mg(2+) and Ca(2+) ions, ethylenediaminetetraacetic acid, ethylene glycol tetraacetic acid and citrate. Inhibited by Al(3+), Fe(3+), Co(2+), Cu(2+), Zn(2+), Pb(2+) and Ag(+) ions, iodoacetate, 4-chloromercuribenzoate and N-bromosuccinimide. kcat is 63.8 sec(-1) for cellobiose. kcat is 52.1 sec(-1) for lactose. Optimum pH is 7.5. Optimum temperature is 30 degrees Celsius. Belongs to the cellobiose 2-epimerase family.