In a small bowl stir together the cayenne, salt and sugar. Add pork and pork belly to a large bowl. Evenly sprinkle over the pork pieces, tossing to combine. Cover and refrigerate for at least 1 hour and up to overnight to marinate.
Remove the pork from the refrigerator and let sit at room temperature for about 30 minutes. Heat a large (7-quart) Dutch oven over medium heat, add the lard (or vegetable oil) to the pot followed by the marinated pork.
Arrange the onion, jalapeño, garlic, orange and bay leaves in the pot then top with the milk and 2 cups of water. The pork should just barely be covered by the liquid.
Bring to a boil over medium heat then lower heat to medium-low and simmer, uncovered, until the meat is fork tender and the water and milk have evaporated, stirring about every 30 minutes for a total of 2 hours.
If the liquid has not all evaporated at this point, remove the meat to a bowl and continue to simmer until it has then add the meat back to the pot if necessary. Remove and discard any remaining onion, jalapeño, orange and bay leaves.
Increase the heat to medium-high heat and fry the meat, stirring occasionally until it is crispy and golden brown on the outside, about an additional 10 minutes. Remove to a large bowl and set aside. (If there is not enough fat to fry the carnitas, spread on a baking sheet and broil in the oven until crispy, about 3 minutes).
For serving:
Use a slotted spoon to top the tortillas with a scoop of the stewed pinto beans followed by pieces of carnitas and top with pico de gallo and pickled onions. Serve with lime wedges.