Rinse Fuyu persimmons. Trim and discard stem ends. Slice persimmons crosswise into thin rounds; you should have 8 cups.
In a large bowl, combine persimmons, granulated sugar, brown sugar, tapioca, cinnamon, orange peel, lemon peel, and lemon juice; stir gently to blend.
Fit 1 pastry round into a 9-inch pie pan. Pour in persimmon mixture and dot with butter.
Lay remaining pastry round over fruit. Fold pastry edges together and crimp to seal. Cut decorative slits in top pastry.
Bake on the lowest rack in a 375° oven until juices bubble in center of pie and pastry is well browned, about 1 hour. If pastry edges brown before pie is done, drape dark areas with foil. Cool pie on a rack. Serve at room temperature.