Mix cayenne, salt, and sugar in a bowl. Toss the pork shoulder and pork belly pieces with the spice mixture, cover, and refrigerate for at least 1 hour or overnight.

Remove pork from the fridge and let sit at room temperature for 30 minutes. Heat a large Dutch oven over medium heat, add the lard, then add the seasoned pork.

Arrange the onion halves, jalapeño, smashed garlic, orange halves, and bay leaves in the pot. Pour in the milk and 2 cups of water — the pork should be just barely covered. Bring to a boil, then reduce heat to medium-low.

Simmer uncovered until the meat is fork-tender and the liquid has almost fully evaporated, about 2 hours, stirring every 30 minutes. Discard the onion, jalapeño, orange, and bay leaves.

Increase heat to medium-high and fry the pork in the remaining rendered fat, stirring occasionally, until the edges are crispy and golden brown, about 10 minutes.

Pile crispy carnitas onto warm tortillas and top with pico de gallo and pickled red onions. Serve with lime wedges.