Position an oven rack in the center of the oven and preheat to 375 degrees F.
In a medium bowl, toss the sliced apples with the lemon juice until the apples are thoroughly coated. Add the raisins, 1/4 cup sugar, and the 2 tablespoons cold cubed butter and toss well. Set aside.
Lightly dust the counter or work surface with flour. Lay the puff pastry on top and dust the rolling pin with additional flour. Gently roll the puff pastry to 1/8-inch thickness.
Spread the apple and raisin mixture over the bottom half of the puff pastry square leaving about 1-inch of space along the side edges. Fold the top half of the puff pastry over and pinch to seal the edges together.
Brush the entire strudel with the melted butter and then sprinkle with cinnamon and remaining sugar. Using a serrated knife, make 3 diagonal slits across the top of the strudel.
Place the strudel on a parchment lined baking sheet and bake for 40 minutes, rotating halfway through cooking, until the pastry is puffed and golden brown.