To a large pot, add the cubed pork shoulder, onions, avocado leaves, pepper, salt, garlic, and bay leaves. Add enough cold water to cover all the meat. Bring to a boil over high heat, then continue to boil for 20 minutes.
Add the orange juice, milk, and cola, return to a boil, and simmer until the liquid has reduced by half, about 1 hour.
Add the lard, let it melt, then boil off the rest of the liquid until the meat begins to fry, 1 hour more.
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Once the meat turns dark golden brown and is crispy, scoop it out of the pot and onto a paper bag or paper towel-lined baking sheet to drain.
Serve with corn tortillas, guacamole, pickled vegetables, cilantro, lime wedges, cilantro rice, and pinto beans.