Cut apple halves crosswise into 1/16-inch-thick slices and transfer to a bowl.
Bring water, sugar, lemon juice, and butter to a boil in a small saucepan, stirring until sugar is dissolved, then pour over apples. Turn apples until slightly wilted, then drain in a colander set over a bowl, reserving liquid.
Preheat oven to 425°F.
Roll out pastry sheet on a lightly floured surface into a 121/2-inch square and cut out 4 (6-inch) rounds. Transfer rounds to a lightly buttered baking sheet and top with overlapping apple slices. Bake in middle of oven until golden brown, about 25 minutes.
Boil reserved liquid in saucepan until reduced to about 1/3 cup, then brush on baked tarts.
