Margaret,
I think that since it is a part of a lyme protocol (Dr. K uses Stephania as one of the 5 herbs to treat lyme and co-infections), I would say it is possible to cause a herx, but you can start at low doses--I guess for you that would mean 1/10 of a drop, if there is such thing :)
This is a website that lists 10 items (and a lot more if you scroll down) that help with asthma (they mention Licorice, too) that may not give you a herx because they doesn't target lyme specifically:
http://www.natural-homeremedies.com/homeremedies_asthma.htmYou can find more natural remedies if you scroll down including nutrition tips to prevent symptoms of asthma. It's worth a try--they are things that are easy to get or you may even have them in the house already.
Maybe you can find better websites, I just pulled this up right now and I would say honey and ginger are pretty safe to use--maybe you can mix some with Licorice? Dried ginger is not as effective, so if you get some fresh root ginger and shave it, it is much more effective.
Reishi seems to be an anti-viral and a immune booster, so maybe that's why you are experiencing a herx. Maybe you can use it slowly and build up? It may hit the virus you are dealing with and that's hy you are herxing? More about
Reishi here:
http://www.webmd.com/vitamins-supplements/ingredientmono-905-REISHI%20MUSHROOM.aspx?activeIngredientId=905&activeIngredientName=REISHI%20MUSHROOMI hope this helps and I am so sorry you are dealing with this on top of everything else!
Hugs