Step 1: Solve this from the common name clue itself: dog lichen. In lichenology, this name is specifically tied to Peltigera canina, whose lobed thallus bears tooth-like rhizines that were fancifully compared to a dog's canine teeth.
Old herbal medicine, going back to the doctrine of signatures style reasoning, used Peltigera canina, sometimes combined with pepper, as a remedy against rabies (hence hydrophobia was the old term for the disease), giving this lichen its common name.
The remaining genera, Lobaria, Ochrolochia and Evernia, are lichens known for other economic or folk-medicinal uses (bronchial remedies, dye/perfume fixatives) but are not called dog lichen and are not linked to the rabies treatment tradition. Answer: Peltigera.