Remove the pork butts from refrigeration 1 hour before cooking. Do not remove the bone.
Heat the lard in a large stainless steel pot over high heat to 250 degrees F. The pot needs to be large enough to fit all the pieces of pork butt side by side, not on top of each other, and preferably not touching each other. Add enough lard to completely submerge the meat. Add the onion and garlic and let brown but do not burn. If garlic burns, you must start the process over. Remove onions and garlic from the lard and discard.
Carefully add the pork pieces to the lard and then allow the oil to reach 250 degrees F again. Do not let the pork stick to the bottom or sides of pot. Stir around every 30 minutes to insure even coloring. Cook for approximately 1 to 1 1/2 hours. The pork should be caramel-colored with an internal temperature of 170 to 180 degrees F on an instant-read thermometer.
Five minutes before you are ready to remove the meat, sprinkle the kosher salt into the oil. Continue to cook pork for 5 more minutes and then remove the pork from the oil to a platter. Cover and let rest for 15 minutes.
Shred the meat and serve with Pico de Gallo, warm tortillas, salsa, limes, and radish slices.
Combine all ingredients and season with salt and pepper, to taste. Let sit for 15 to 20 minutes. Serve.