Asthma is an inflammatory disease of the lungs and the air passages often caused by some inflammatory trigger, such as environmental allergins, pollen, dust, etc., cats, and dogs or respiratory infection or other viruses. But it also can be caused by dietary factors including the two most common, dairy and gluten, which trigger food sensitivities and food allergies that lead to inflammation in the lungs.
Therefore: I do recommend a trial of a gluten and dairy free diet to see if it improves asthma.
The most effective approach for significant asthma would be The Ultra Simple Diet, which is a comprehensive food allergy and sensitivity elimination diet. Short of that, you can try a gluten-dairy free diet for at least 6-weeks to see if it makes a difference.
Often digestive issues may contribute to asthma including irritable bowel, a change in the gut bacteria, which can lead to inflammation. Changing your diet will help, as will taking probiotics that can help balance the bacteria in your gut.
Other causes of asthma may include reflux, but in my experience diet is one of the most powerful tools to address this.