Heat the oil in a 10-inch straight-sided sauté pan over medium heat. Add the apple to the pan and cook until lightly browned, approximately 1 minute.
Increase the heat to high and add the apple juice, caraway seeds, salt, pepper, and cabbage to the pan. Cover the pan and shake to toss the cabbage to coat.
Reduce the heat to low and cook for 10 minutes. Remove the lid and cook for an additional 5 minutes.
Add the lemon juice and butter just before serving. Serve immediately.