Peel papayas, cut in half lengthwise, and discard seeds. Cut papayas lengthwise into 2- to 3-inch-wide slices, then cut crosswise into 1/4-inch-thick strips. Measure 8 cups of fruit; reserve extra for other uses.
In a large bowl, mix sugar, cornstarch, coriander, cardamom, nutmeg, and lemon peel. Add papayas and lemon juice, and mix.
Unfold 1 pastry round and ease into a 9-inch pie pan. Fill pastry with fruit mixture.
Unfold remaining pastry on a lightly floured board and roll into a 13-inch-wide round.
Center round over fruit. Pinch pastry at rim to seal, then fold edge under itself, flush with pan rim, and pinch to flute. Slash pastry top decoratively. Set pie on a foil-lined baking sheet.
Bake on the bottom rack of a 375° oven until juices bubble near center, 1 hour and 10 minutes to 1 hour and 20 minutes (55 to 65 minutes in a convection oven). If pastry edges get too dark, cover loosely with foil. Cool at least 1 hour. Cut into wedges.