Halve the leeks lengthwise and cut into 1-inch pieces. Halve the artichokes lengthwise. Heat the olive oil in a large skillet over medium-low heat, add the leeks, and cook until soft but not browned, stirring frequently, about 5 minutes. Remove the leeks from skillet and set aside. Increase heat to medium and add the artichokes. Cook about 3 minutes per side. Return the leeks to skillet and toss to mix. Stir in the lemon juice, salt, and pepper. Cook the linguine according to the package directions, reserving ½ cup of the pasta water. Transfer to a large bowl. Add the vegetables to the linguine and toss with half the Parmesan. Add some of the pasta water to moisten, if necessary. Sprinkle with the remaining cheese.