Put tripe, pig’s feet, onion, garlic, and salt in a large stockpot and add the water. Bring to a simmer over medium heat and cook until the tripe is tender, about 3 hours.
Meanwhile, if using ancho chiles, put them in a small saucepan, add water to cover, and bring to a boil. Boil until softened, about 10 minutes. Drain and let cool slightly, then peel off the skin, put the chiles in a blender and puree.
Add the pureed chiles (or the chile powder), hominy, and oregano to the soup. Reduce the heat to low, and cook for another 30 minutes.
Ladle the soup into bowls, and serve with the onion and lemon on the side, along with tortillas. One tablespoon of diced onion should be stirred into each bowl of soup, and the juice of the lemons added to taste.