Given the information about the thyroid problem, I agree with the advice about trying to get your father to visit a medical practitioner, and recognise that is very difficult.
The diet your father is eating sounds very low in calories (to me). It sounds as if he has removed a lot of the starch from his diet but it has not been replaced with fat. Vegetables and fish are generally fairly low in calories. Will he eat nuts at all? Tree nuts (i.e not cashews and peanuts) are generally low in carbohydrate and fairly high in calories.
The diet your father is eating sounds very low in calories (to me). It sounds as if he has removed a lot of the starch from his diet but it has not been replaced with fat. Vegetables and fish are generally fairly low in calories. Will he eat nuts at all? Tree nuts (i.e not cashews and peanuts) are generally low in carbohydrate and fairly high in calories.