Preheat the oven to 350 degrees F. Butter a 9-by-13-inch baking dish and set aside. Bring a large pot of salted water to a boil. Add the noodles and cook until softened but not cooked through, 3 to 4 minutes; drain and transfer to a large bowl.
Meanwhile, whisk the eggs and egg whites in a medium bowl until well combined. One at a time, whisk in 3/4 teaspoon salt, the chiles, lemon juice and melted butter. Stir in half of the artichoke hearts and 2 cups grated cheese. Pour the egg mixture over the noodles and mix well with your hands.
Transfer the noodle mixture to the prepared baking dish. Top with the remaining artichoke hearts and 1 cup grated cheese. Bake until golden brown, about 1 hour. Let cool at least 30 minutes before serving.