In a bowl stir together the cayenne, salt and sugar. Sprinkle over the pork shoulder and pork belly pieces, tossing to combine. Cover and refrigerate for 1 hour and up to overnight.
Add to Dutch oven or pot
Remove the pork from the refrigerator and let sit at room temperature for 30 min. Heat a large Dutch oven over medium heat, add the lard to the pot followed by the pork.
Add remaining ingredients
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 tender and the water and milk have evaporated, stirring occasionally for 2 hours.
Fry in fat
Increase the heat to medium-high heat and fry the meat, stirring occasionally until crispy and golden brown on the outside, about an additional 10 min.
Assemble tacos and serve
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 limes.