Preheat oven to 175 degrees C. Coat a 22cm x 32cm baking pan with cooking spray.
Beat together cake mix, lemonade and melted butter until a soft dough forms. Press half the dough evenly into the bottom of the prepared pan.
Beat together cream cheese and white sugar in a bowl until creamy. Add egg and beat again. Spread cheesecake over the dough in the pan.
Place strawberry jam in a microwave-safe bowl. Heat in the microwave until melted, about 30 seconds. Drop by small spoonfuls all over the top of the cheesecake layer. Drag a knife very carefully through the cheesecake to swirl in the strawberry jam.
Take a small piece of the remaining dough and press it flat in the palm of your hand. Rip the dough into pieces and scatter over the cheesecake, covering as much of the surface as you can.
Bake in the preheated oven until golden brown, about 30 minutes. Remove from the oven and cool on a wire rack for 2 hours. Refrigerate until completely chilled, about 4 hours to overnight.
Stir the icing sugar and lemon juice together in a bowl. Drizzle mixture over the chilled cheesecake and top with sprinkles. Let icing set, about 15 minutes. Cut into 24 bars.