Wash and cut 2 of the lemons into paper-thin slices. (It is very important to slice the lemons as thinly as possible; use a very sharp knife or an electric meat slicer, if one is available.) Remove the peel and pith of the remaining lemons; slice the flesh very, very thinly, and put it with the other slices in a large mixing bowl. Add the sugar and toss well to coat all the lemon slices. Cover the bowl with plastic wrap and let the mixture rest overnight, stirring occasionally. This takes the bitterness from the rind.
The next day, preheat the oven to 450 degrees. Press one Pate Brisee round into a 9-inch pie plate and chill.
Add the beaten eggs to the sugar-coated lemon slices and mix well. Turn the mixture into the prepared pie shell, neatly arranging some of the lemon slices on top. Cut long, even slashes 1 inch apart in the other pastry round and cover the filling with it. Crimp the edges of the pie to seal. Brush the pastry top and edges with the egg white and sprinkle with sanding sugar. Bake for 20 minutes. Cover the edges of the pie with foil. Reduce the oven temperature to 375 degrees and continue baking until the crust is golden brown and shiny, about 30 minutes. Let cool on a rack before serving.