I wouldn't allow the dog to eat anything I was unsure of. Contrary to belief, they do not have cast iron stomachs, and WILL eat things not good for them. (like dog beds getting chewed and entwined in their intestines)
There are some things WE can eat, but they can't, like baker's chocolate and tylenol.
Also, some mosses and lichens like Old Mans Beard and Reindeer moss can be very beneficial, and used in medications and foods.
Other's can KILL like Wolfen Lichen, which looks similar to harmless varieties. Wolf Lichen got it's name for killing Canis Lupus!
So, like mushrooms, I would beware and not take the risk.