Mix 1/2 cup cornstarch, l- l/2 cups sugar, water and egg yolks in saucepan over medium heat. Stirring constantly, bring mixture to a boil (about 8 to 10 minutes), reduce heat and continue stirring for one minute until very thick. Remove from heat; stir in lemon juice, lemon zest, and butter until smooth. Pour hot filling into baked pie crust.
Beat egg whites in mixer at high speed, until soft peaks form; gradually add 1/2 cup sugar and 2 teaspoons cornstarch, beating until stiff peaks form (tips stand straight) about 3 minutes. Top pie by spooning meringue over hot pie filling, making sure meringue touches edge of pie crust to seal. Use the back of a spoon to swirl meringue and draw up into peaks.
Bake: Place oven rack in bottom third of preheated 375 degrees F oven. Bake 10 minutes, until peaks are lightly browned. Cool at room temperature for 30 minutes. Chill for a minimum of 3 hours before serving.