My personal diet is vegetarian, working on vegan, and has been for over 30 years, for moral reasons. I don't eat my friends. The most important advice is to eat a balanced diet, which would include fruits and vegetables, and exercise. There are no hard and fast rules.
If your father is struggling with weight perhaps an appointment with a good nutricionalist would be a good idea. If certain foods cause inflammation for your father, then certainly he should cut back on those, but not all people react to foods the same way. I react to some dairy (fine with me because I eat very little of it - a little yogurt and sometimes a lot of ice cream), but no problems with gluten or sugar.
It sounds like your father should work with someone and experiment with foods a bit. There are some here who follow very rigid eating guidelines - all different - and believe in them, which is fine. Let your father find what works best for him in terms of weight gain and enjoyment. Do make sure that none of his meds interact with any foods or supplements. Grapefruit is a big one. I finally went off of the last of the pills in my collection with a no grapefruit sticker!
While on watch and wait, I maintained a normal healthy diet, lower fat, more fruits and veggies, moderate protein, less sugar, and very limited processed foods, but basically ate what I wanted within reason. I, too, was losing weight and needed to eat to keep from losing more. Sometimes you need to eat what your body needs. Especially when you do not have an appetite.
I eat vegan and this has meant my weight has remained steady. Try adding some nuts with fruit, also avocado. Porridge made with coconut milk is delicious. We’re all different, so trying different things and finding what works best is key. Good luck.
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