Toast the dried chilies by putting them in a preheated 200-degree oven for 3 minutes; you should smell them toasting when you open the oven door. (If using canned chipotles, toast only the Ancho.) Remove the toasted chilies from the oven and open them up. Remove and discard the seeds and stems. Place the chilies in a bowl and cover with hot water.
When chilies are soft (after about 15 minutes), remove them from the water and place them (or the Ancho and the canned Chipotle) in the work bowl of a food processor, along with the garlic, lard, cumin, cloves, salt, and pepper. Pulse to make a rough paste. Rub the paste all over the pork loin with your fingers. Cover the rubbed pork and refrigerate for 8 hours.
Remove it from the refrigerator 1 hour before you're ready to put it in the oven. Make a bed of half the sliced onion in the clay pot. Lay the marinated pork loin over it. Cover the pork with the remaining onion. Most clay pots call for soaking the lid and then placing the entire pot, with food inside, in a cold oven before turning on the heat. Follow the instructions for your pot. In any case, the oven should be set at 300 degrees.
Once the oven is hot, cook the roast for 1 hour. Do not open the pot. After an hour, remove the roast from the oven. Let it sit in its broth for 10 minutes. Slice the roast thinly and serve.