Taking Care of a Lame Dog

My Labrador retriever, Rover, is going to hit the double digit age next month.  Although I have cared for him with all my love I cannot prevent the signs of old age dawning upon him.  I have noticed recently that he is suddenly beginning to limp on his rear right foot.  It must be signs of arthritis.  I took him to his vet yesterday and had him examined.  The vet even took x-rays of all the joints.  But the diagnosis did not reveal anything that would indicate arthritis is the cause.  The vet is at a loss and cannot offer a proper explanation.  I am considering taking Rover to another vet, who is more of a specialist.  In the meantime I am wondering if I can help Rover with any kind of dog outdoor wear. Maybe a stiff sock all the way up the right rear leg will help him bear his pain and enable him to walk and run better.