Heat the oven to 350°F and whisk 1 cup sugar, the cornstarch, salt and water in a saucepan.
Cook over medium heat until thick and bubbling, whisk 1 cup of the hot mixture into the egg yolks, then return everything to the pan and boil for 1 minute.
Remove from the heat, stir in the lemon juice, zest and butter, and immediately pour the hot filling into the crust.
Beat the egg whites and cream of tartar to soft peaks, gradually add the remaining 1/2 cup sugar, and beat to glossy stiff peaks.
Spread the meringue over the hot filling all the way to the crust edge and bake for 10 to 12 minutes until browned and 160°F.
Cool for 1 hour, then refrigerate for 3 hours before slicing.