I’d start with the question of whether either of the doctor’s suggestions are actually necessary. Cholesterol is complicated. HDL is the “good cholesterol”. LDL is the “bad” cholesterol but it turns out there are two kinds, one of which is a large fluffy particle and the other which is small and dense. Only the small dense ones are at all linked with arterial disease, but the standard tests don’t distinguish, making them basically useless. People doing keto typically have a much lower small particle count, even though their total LDL may be higher than normal. (in other words, you may never “get his cholesterol down” doing keto, and it totally doesn’t matter, if he has a low small particle count.)
In order to add body fat it’s necessary to have insulin in the picture, which comes about when we eat carbs. So you might get his weight up a bit by adding some healthier carbs - fruit, legumes. But is it really necessary?
ETA: If you want him in keto and he’s afraid of animal fat, load up on organic olive and coconut oil instead.
Edited again, sorry: I don’t know what fat does to small particle size cholesterol if a person isn’t in ketosis. If you can’t actually get him to commit to a ketogenic diet - which is all the time, not just specific meals - I don’t know what good or bad effect fat loading would have.