One of the surprising benefits my husband and I experienced when we started eating low carb (high fat) was a big reduction in our asthma. Mine's environmentally induced, and I'm at the point where I can just avoid my triggers, so I didn't notice this until a few months later when we visited my inlaws's cat-, dog-, and smoke-infested house. No asthma for me at all, whereas previously I was always miserable at their house, having to stay outside in the back or hide in the kitchen, the only room without carpet. What a wonderful change to sit in the living room with the whole family, and not have any symptoms!
My husband, on the other hand, went from using his inhaler multiple times a day to just a few times a month--his asthma has always been much worse than mine, and now ten years on he still uses it just as infrequently.
The main change in our diet was to cut out sugar and grains, and we added in more animal fats such as butter, cream, and lard. (We had some other unrelated improvements to our general health too, besides losing weight; for instance, my husband's migraines became far fewer and much less severe. We originally made the change in order to control my diabetic husband's blood sugar.) I don't know if it will work for everyone, but it worked for us.