Roll half of pastry to 1/8-inch thickness on a lightly floured surface; fit into a 9-inch pie plate. Set aside.
Combine sugar, flour, cinnamon, and nutmeg in a small mixing bowl. Set aside.
Arrange half of mangoes in pastry shell; sprinkle with half of sugar mixture. Repeat layers. Sprinkle with lemon juice; dot with butter.
Roll remaining pastry to 1/8- inch thickness; place over filling. Trim edges; seal and flute. Cut slits in top crust to allow steam to escape. Bake at 425° for 10 minutes on lowest oven rack. Reduce heat to 350°; bake an additional 35 minutes. Cool.