Preheat oven to 400 degrees F. Combine 1/4 cup sugar and cinnamon in a small bowl. Pulse apples, remaining 1/2 cup sugar, lemon juice, and salt in food processor until chopped finely. If you don't have a food processor you can grate the apples on the coarse side of a box grater. Let apples drain in a colander for 5 minutes. Transfer apple mixture to a bowl and add applesauce. I sprinkled a little cinnamon in the apple mixture as well.
Unfold 1 sheet puff pastry onto lightly floured work surface and roll into 10-inch square. The pastry sheet measured 10 inches by 9 inches, so you only need to roll one end. Cut into 4 squares. Fill each turnover with 2 Tbs. apple mixture, brush edges with reserved apple juice, then fold and crimp. Place turnovers on a plate and freeze until firm, 15 minutes.
Spray baking sheet with non-stick cooking spray. Place turnovers on baking sheet and brush tops with reserved apple juice and sprinkle with cinnamon sugar. Bake until well brown, 20 to 25 minutes. Serve warm or at room temperature. Drizzle with confectionary sugar glaze.