In a food processor (or large bowl) sift together flour, sugar and salt. Add butter and either pulse a few times or work the butter gradually into the flour mixture with your fingers until the pieces are the size of walnuts. Add egg, pulse a few more times or mix into the mixture until the mixture holds together when you squeeze it with your finger. Add the water if necessary to reach the proper consistency. Turn the dough out onto a board and form it into a round disk. Refrigerate 1 to 2 hours.
After the dough has chilled, remove from refrigerator and roll it a little larger than a 9-inch pie pan and about 1/8-inch thick. Place the dough in the pan. Trim the edges with a knife. Refrigerate again for 1 to 2 hours.
Preheat the oven to 375 degrees. Dock the dough with a fork. Line the dough in the pan with aluminum foil, fill with dried rice or beans. Bake for 15 minutes. Remove the foil and weights.
Bake 10-15 minutes more until the crust it lightly browned. Cool to room temperature.
To make the filling:
In a saucepan, add 1/2 cup water, 1/2 cup sugar, salt, lemon juice, lemon zest and bring to boil. In a medium bowl, whisk together 1/2 cup sugar and cornstarch. In another bowl mix the egg yolks and 1/2 cup water together and add to the cornstarch mixture. When the lemon juice boils add a little of it into the yolks whisking. Then add the egg mixture back into the saucepan and over medium heat whisk constantly until the mixture thickens. Remove pan from heat. Add butter, stir until melted and incorporated. Pour immediately into pre-baked crust. Cool to room temperature.
To make Meringue topping:
Preheat oven to 325 degrees. In the bowl of an electric mixer beat the egg whites until they begin to foam. Reduce the speed of the mixer. Gradually add the sugar, a tablespoon at a time, until it dissolves into the egg whites. You should feel no grit. It should take about 3 minutes. Then increase the speed and beat until medium stiff peaks. Dollop the meringue on top of the pie, beginning at the crust. Swirl with the back of a teaspoon to make peaks. Or, pipe a lattice design across the top. Sift a little confectioners sugar over the top. Bake for 20 minutes (checking and turning the pan every 5 minutes) until the crust is golden all over. Cool to room temperature before serving.