Generously sprinkle the pork shoulder with salt and pepper. Heat the oil in large nonstick skillet set over high heat. Sear the meat on all sides until deeply browned, about 3 minutes per side.
Transfer the pork to a slow cooker. Add the almond milk, broth, oregano, garlic, carrots, celery, bay leaves, lemon peel and onions. Set the slow cooker to low, then cover and cook until the meat can be easily pulled apart with a fork, 6 to 8 hours.
Transfer the pork to a work surface and use two forks to shred the meat. Strain the cooking liquid and reserve. Transfer the pork to a serving platter, then ladle the cooking liquid over the meat and season with salt and pepper as needed.
Place the avocado slices, lettuce leaves, half of the lime wedges, the cilantro sprigs and red onion slices on a platter. Squeeze the remaining lime wedge over the avocados to prevent discoloration. Have guests build their own carnitas lettuce wraps.