Position a rack in the lower third of the oven and preheat to 450 degrees. Lightly oil a large, rimmed baking sheet or shallow baking pan.
Toss the potatoes with 2 tablespoons of the oil in a large bowl. Spread on the baking sheet. Bake for 15 minutes. Turn the potatoes with a metal spatula and bake for 15 minutes more. Toss the artichokes with the remaining 1 tablespoon olive oil and mix into the potatoes. Continue baking until the vegetables are tender and lightly browned, about 20 minutes more.
Transfer the potatoes and artichokes to a large bowl. Sprinkle with the lemon zest, then the lemon juice and parsley. Season with salt and pepper. Mix gently and serve hot in the bowl or on a platter.