Heat the vegetable oil in a large Dutch oven until it shimmers, and sear the beef and pork roasts on all sides until browned, about 3 minutes per side.
Pour the water over the meat, cover, and cook in the preheated oven for 2 hours. Uncover the Dutch oven, and remove and discard the bones from the beef roast. With a spoon or spatula, loosen the browned flavor bits from the bottom of the Dutch oven.
Mix together the ketchup, mustard, Worcestershire sauce, lemon juice, and salt and pepper in a bowl. Pour the ketchup mixture over the meat, stir to combine with the browned flavor bits, and cover the Dutch oven.
Reduce oven heat to 250 degrees F (120 degrees C), and cook for 2 more hours. Shred the meat with 2 forks, pile each bun with about 1/3 cup meat and sauce, and garnish with onion and pickles to taste.
