Scrape off as much of the lichen as possible using the scraper. Scrape right into the shingle if necessary to fully remove as much of the lichen as you can. Lift up the shingle and scrape out any lichen growing underneath or any rotted material. Scrub the surfaces with an even mixture of bleach and water.
Place roofing caulk on the rear of a shingle, on the top half, and position it so that half of it overlaps the bottom edge of the lichen-covered area and the other half is on unaffected shingles.
Nail the shingle in place, placing two nails every 12 inches or so in two rows across the top of the shingle.
Apply the caulk in the same manner to another shingle, and set it above the first shingle, one step back and deliberately off-center. Nail it in place.
Attach a third shingle in place by applying caulk on the rear and sliding the top of the shingle up underneath the bottom flaps of another shingle, so that it is overlapping the second shingle part way but still covered by the shingle that overlaps it. Secure it in place with roofing nails where possible.