Preheat the oven to 350 degrees F (175 degrees C). Line a 9x13-inch baking pan with parchment paper.

Unroll both pieces of crescent dough. Lay one piece on the bottom of the prepared pan. Set second piece aside.

Combine cream cheese and 1/2 cup white sugar in a bowl; beat with an electric mixer until smooth. Mix in lemon pie filling, lemon zest and juice, and vanilla extract. Pour over crescent dough in the baking pan and cover with the second piece of dough. Pour melted butter over top and sprinkle with remaining white sugar.

Bake in the preheated oven until golden brown, about 25 minutes.

Remove from the oven and place on a wire rack until completely cool, about 30 minutes.

Chill in the refrigerator for at least 3 hours, or overnight.