1. Cook cabbage and onion in hot oil in a large nonstick skillet or Dutch oven over medium-low heat, stirring occasionally, 30 minutes.
2. Meanwhile, peel and chop apples; toss with lemon juice. Stir apple mixture, sugar, salt, and pepper into cabbage mixture. Cook, stirring occasionally, 30 minutes.
Red Cabbage and Pears: Prepare recipe as directed, substituting Bartlett pears for apples.