That's correct - the chewable has no lactose. It does have other inactive ingredients, and may itself trigger a rash or reaction.
Bottom line is, if it triggered a reaction, some other asthma preventative must be considered. When your child is in better overall shape, you should talk to your doctor about re-challenging, but only with careful medical supervision and preferably in very small, increasing quantities (e.g., 1/8 of a pill at a time).
Mark