Asthma is one of those systemic issues that needs to be dealt with on all levels - emotional, physical, spiritual. There are often past-life issues involved.
The physical side of things includes a need for Omega 3 and 5's (essential fatty acids) so that the proper prostaglandins for relaxation can be manufactured by the body.
If there is any kind of phlegm involved, then a heating/pungent diet is required to get rid of excess.
Vitamin A, C, E, zinc - the usual skin food - helps the lung tissue repair itself. Ginger, garlic, onion, pineapple juice or bromelain supplements, are excellent natural anti-inflammatories.