Place a large baking pan in oven. Preheat oven to 450°F.
Toss carrots, Brussels sprouts, onion with oil, rosemary, salt, and pepper in a large bowl. Arrange vegetable mixture and sausage on preheated pan in a single layer. Bake in preheated oven until just tender, about 20 minutes.
Preheat broiler to high. Add apple to pan; broil until apple is tender and vegetables are slightly caramelized, 5 to 6 minutes. Remove pan from oven. Squeeze lemon over pan and sprinkle with parsley.