They have their own instincts and rituals. Many animals like cows for instance chew cud. The others chew various grasses that generally remove the leftovers from dental crevices. Most importantly, chewing produces salivation, which is nature's own super cleanser. Saliva is an astringent and a wound healer.
Animals therefore manage to remain clean without the use of soap, toothpastes and toothbrushes.
The fungi need the algae for food and the algae need fungi for protection. They have no leaves, stems or roots. They grow slowly on hard surfaces as rocks and walls and can live for thousands of years. But the worst enemy of most lichen is pollution. They are sensitive to air pollution so they are found in places where the air is cleanest.