Melt the butter in a large frying pan, add the mushrooms and sprinkle with salt and freshly ground pepper. Cook for about 3 minutes, stirring regularly. Pour in the tomato juice and Worcestershire sauce and add the paprika. Bring to the boil then reduce the heat and simmer for about 10 minutes.
Meanwhile, place the lamb chops or cutlets on a grill pan (broiler pan), season with salt and freshly ground pepper and grill for 4 or 5 minutes on each side. Place the meat on a serving dish and spoon the mushrooms and sauce over them.