My rhododendrons are about 40 years old and are starting to die out. There is a great deal of lichen on the branches .Is this killing the plant? What is the best way to remove it?
No. The lichen just sits on it. The dying out will be due to something like root rot (water molds) or honey fungus, or being overtaken by evergreen trees.
You can spray with lime sulphur in the dormant season. That will control the moss and lichen growing on trees and shrubs. Use a scrub brush and don't damage the bark.