Hello, This is Dr. Klarida Papaqako answering your question. I read very careful your concern. Some of the causes of that may cause a painless lump in the position you are describing may be: 1) Epidermoid or sebaceous cysts, who are soft, not painful, and feel like a lump under the skin. 2) If its deeper than the skin, near the joint, and your father has problems chewing, it may come from the temporo-mandibular joint. The joint might have hurted some time before this or may cause pain while chewing now. 3) In that place there are located the salivary glands and the parotid gland. So in their problems, like stones, blockage, or tumors, the first and only sign in general can be a non-painful lump not movable. Consider for sure checking it to his physician. Hope this helps, Take care.