You can cut strips of zinc flashing (copper and lead work, too) and slide them under a course of roof shingles to kill lichen and moss growing there, or you could just buy these premade strips from Shingle Shield
. The premade ones are much quicker and probably neater looking.
It's not a bad idea to suggest to customers that overhanging tree branches are what's keeping their roof moist in the first place and allowing the vegetation to grow. Pruning the surrounding trees will let the roof and the rest of the building dry out more quickly.