Can leg claudication ever get better on its own?

With exercise. Claudication symptoms can be improved with exercise. With a regular program exercise endurance can improve. It is unlikely for symptoms ro go away on their own.
With exercise. Claudication can get better with exercise. Why? Because exercise improves the muscles ability to utilize oxygen efficiently. Athletes can run a marathon at high speeds because they trained their leg muscles. Similarly, although claudicants are unlikely to run a marathon, they can, with training, eventually walk long distances without pain. Not smoking, eating well, and medical treatment help too!