Both eczema and asthma are auto-immune, pro-inflammatory diseases and are some how linked. Even though the underlying common mechanisms between the two aren’t understood working in general with an anti-inflammatory diet may help a great deal. Omega 3 fatty acids from fish oil and citrus fruits high in antioxidant filled bioflavinoids are also as well.
http://www.sciencealert.com.au/news/20080807-17623.html
“The incidence of asthma in people from the ages of 8 to 44 who had childhood eczema, was nearly double that of people who had never had eczema,’’ Dr Burgess said.