Catalyzes the interconversion of L-rhamnose and L-rhamnulose. L-rhamnopyranose = L-rhamnulose Binds 1 Mn(2+) ion per subunit. Carbohydrate degradation; L-rhamnose degradation; glycerone phosphate from L-rhamnose: step 1/3. Belongs to the rhamnose isomerase family.