Preheat oven to 375° with rack on bottom rung. On a lightly floured board, stack 2 pastry disks (enough for a 2-crust pie) and roll into a 13-by 18-in. rectangle, applying a little more pressure at edges to even out corners. Fit pastry into a 10- by 15-in. jelly roll pan*, filling corners; don't trim edges. Chill. Reflour board, stack remaining pastry disks, and roll into a 12- by 17-in. rectangle. Sprinkle a large flat baking sheet with flour, set pastry on baking sheet, and chill.
In a large bowl, combine lemon zest and juice, cornstarch, granulated and brown sugars, and cinnamon. Add persimmons and stir to coat. Pour into pastry-lined pan.
Over the center of flat pastry, cut several rows of decorative slits, using an oval 1 1/2- by 2-in. cookie cutter* turned on a diagonal, or a small knife. Carefully transfer pastry over persimmons. Pinch edges of top and bottom crusts together to seal, tucking under extra pastry. Crimp edges just inside pan rim. Lightly brush pastry with water, then sprinkle with sparkling sugar.
Bake until crust is golden brown and filling is bubbling in center of pie through slits, 45 to 50 minutes. Let cool on a rack at least 2 hours.
*Pillsbury refrigerated pastry works well. We like Nordic Ware's sturdy aluminum jelly roll pan ($18; nordicware.com), which has a rolled steel rim to help prevent warping. Find Ateco 9-piece oval cutter set at amazon.com.