How to Make It
Preheat oven to 350°F. Stir together cornstarch, lemon juice, and lime juice in a medium nonreactive saucepan until cornstarch dissolves. Stir in 3 cups water, 2 cups sugar, butter, 1/8 teaspoon salt, and lemon zest. Bring to a boil over medium-low, stirring constantly with a wooden spoon, about 15 minutes. (Mixture will thicken as it cooks.) Remove from heat.
Whisk egg yolks in a large bowl. Gradually whisk in hot lemon-lime mixture. Press a piece of plastic wrap directly onto surface, and let cool 30 minutes. Pour mixture into pastry shell. Set aside.
Combine egg whites and remaining 1/8 teaspoon salt in bowl of a heavy-duty stand mixer fitted with the whisk attachment. Beat on medium speed until frothy, about 1 minute. Gradually add cream of tartar and remaining 1/2 cup sugar, beating on medium speed until mixture forms stiff, glossy peaks, about 4 minutes.
Gently dollop meringue over lemon-lime filling. Using the back of a spoon, spread meringue to edges. Swirl decoratively with spoon. Bake in preheated oven until meringue is golden brown, about 20 minutes. Transfer to a wire rack, and let cool to room temperature, about 2 hours. Transfer to refrigerator until well chilled, about 3 hours.