Finely grate the lemon zest into a large bowl. Use a mandoline to slice the lemons as paper thin as possible. Pick out and discard the seeds. Add the lemon slices to the bowl of zest, and add the sugar and salt. Cover, and set aside at room temperature for 24 hours. 

Preheat the oven to 425˚F. Use a lightly floured surface to roll out half the dough to 1/8-inch thick. Gently transfer to a 9-inch pie plate, and trim the edge with a sharp knife, leaving an overhang of 1/2 an inch.

Add the eggs, melted butter, and flour to the lemon-sugar mixture. Mix well, then pour into the prepared pie shell.

Roll the second half of pie dough into a 12-inch round, then drape over the pie filling. Trim it, leaving a 1-inch overhang. Tuck the overhang underneath the edge of the bottom crust, and press the edge to seal. Use a fork to crimp the edge decoratively if you'd like. In a small bowl, beat the egg white until frothy, then brush onto the pie crust. Sprinkle with coarse sugar, then use a sharp knife to cut slits in the crust to allow steam to escape. Bake in the center of the oven for 25 minutes. Reduce oven temperature to 325˚F, and bake an additional 20-25 minutes, until the crust is golden. 

Allow to cool on a wire rack, and serve warm or at room temperature.