In a skillet, melt the butter over medium heat. Add the diced apples, sugar, cinnamon, and lemon juice. Cook until the apples are tender, about 5-7 minutes. Remove from heat and let cool.

Preheat the oven to 400°F (200°C). Roll out the puff pastry sheets on a lightly floured surface and cut into squares, approximately 4x4 inches.

Place a spoonful of the apple filling in the center of each pastry square. Fold the pastry over to form a triangle and press the edges to seal. Use a fork to crimp the edges.

Place the turnovers on a baking sheet lined with parchment paper. Brush the tops with the beaten egg mixed with milk. Bake for 20-25 minutes or until golden brown.

Allow to cool slightly before serving. Enjoy warm or at room temperature.