Combine the sugar and cornstarch in the top of a double boiler. Add the water and stir to combine. In a medium bowl, whisk the lime juice and egg yolks until well mixed; add to the cornstarch mixture and whisk until well blended.
Place the double boiler over 1 inch of boiling water and cook, stirring, until the mixture is thick and no starchy taste remains, about 25 minutes. Turn off the heat and remove the mixture from the hot water. Let cool slightly. Whisk in the grated lime zest, vinegar and butter until completely incorporated.
Pour the mixture into the pie shell, cover with plastic wrap and chill in the refrigerator until cold.
Preheat the oven to 350 °F. In a small saucepan, combine the cornstarch and cold water; whisk until blended. Add the boiling water and place over medium heat. Cook, stirring, until the mixture is clear and thickened. Remove from heat and let stand until completely cold.
In a large, grease-free mixing bowl, beat the egg whites with an electric mixer on medium speed until frothy. Increase the speed to high and gradually add the sugar, beating until the egg whites are stiff but not dry. Reduce the speed to low and add the vanilla and salt. Gradually beat in the cold cornstarch mixture. Increase the speed to high and beat until all the ingredients are fully incorporated.
Spread the meringue over the cooled pie filling and bake for 10 minutes, or until the top is lightly browned.