Catalyzes the reversible epimerization of cellobiose to 4-O-beta-D-glucopyranosyl-D-mannose (Glc-Man). Can also epimerize lactose to epilactose. D-cellobiose = beta-D-glucosyl-(1->4)-D-mannopyranose kcat is 28.5 sec(-1) for cellobiose. kcat is 32.5 sec(-1) for lactose. Optimum pH is 7.0-8.5. Optimum temperature is 35 degrees Celsius. Belongs to the cellobiose 2-epimerase family.