Cut bacon into 1/2-inch pieces and place into a large dutch oven. Cook over medium heat until crispy, then remove bacon and set aside. Reserve all the bacon fat. Cut the onion into slices and cook in bacon fat until translucent and tender. Add the apple and cook until tender.
Quarter, core and coarsely shred the cabbage. Add to the dutch oven and toss with the onions and fat until coated. Add lemon juice, vinegar and allspice. Cover and cook 10 minutes, then uncover, add bacon, toss again to mix and add salt and pepper to taste. Cook a minute or two more until the cabbage is barely tender.