It prevents build up of callus when used each day, but it is slow when used on neglected areas. Any oil will do. It is to keep the moisture in the skin and prevent evaporation. Many oils are not absorbed directly into the skin. Even Vaseline will reduce evaporation, but is not absorbed.
Vegetable oil is absorbed better than mineral oil and animal oil better than vegetable.
Hence lanolin or fish liver oil is probably most effective in nourishing the skin and replacing the deficiency in sebum production, but the main purpose of the oil is to keep the water in. Good hydration keeps the skin more resilient and less easily burnt and traumatized. If there is any muscle weakness it is important to prevent contractures developing. If fingers or toes are already becoming contracted in a flexed position it is important that these contractures be overcome. The presence of contractures increases abnormal pressure on the stretched aspect of the joint.