If using a hand-held mixer, you will need a very deep bowl, and should move the beaters vigorously when beating the egg whites for the meringue, to avoid underbeating the egg whites. This pie is best on the day it's made.
FOR THE FILLING: Whisk sugar, lemon juice, water, cornstarch, and salt together in a large nonreactive saucepan until cornstarch is dissolved. Bring to simmer over medium heat. Whisk in yolks until comined. Stir in zest and butter. Bring to simmer and stir constantly until mixture is thick enough to coat back of spoon, about 2 minutes. Strain through fine-mesh strainer into pie shell and scrape filling off underside of strainer. Place wrap directly on surface of filling and refrigerate until set and well chilled, at least 2 hours and up to 1 day.
FOR THE MERINGUE: Adjust oven rack to middle position and heat oven to 400°F Combine water and sugar in small saucepan. Bring to vigorous boil over medium-high heat. Once syrup comes to rolling boil, cook 4 minutes (mixture will become slightly thickened and syrupy). Remove from heat and set aside while beating whites.
With electric mixer, beat in large bowl, at medium-low speed until frothy, about 1 minutes. Add salt and cream of tartar, and beat , gradually increasing sped to medium-high, until whites hold soft peaks, about 2 minutes. With mixer runnin, slowly pour hot syrup into whites (avoid pouring syrup onto whisk or it will splash). Add vanilla and beat until meringue has cooled and becomes very thick.
Using rubber spatula, mound meringue over filling, making sure meringue touches edges of crust. Use spatula to create peaks all over meringue. Bake until peaks turn golden brown, about 6 minutes. Transfer to wire rack, and cool to room temerature.