For the Crust: In a medium bowl, combine graham cracker crumbs and 1/4 cup granulated sugar. Pour in the melted butter and mix until crumbs are moistened. Press mixture evenly into the bottom of a 9×13 inch baking dish.
For the Blueberry Compote: In a small saucepan, combine blueberries, remaining 1/4 cup granulated sugar, and lemon juice. Cook over medium heat, stirring occasionally, until blueberries burst and the mixture thickens, about 5-7 minutes. Let cool slightly.
For the White Chocolate Cheesecake Filling: In a large bowl, beat softened cream cheese until smooth. Gradually beat in sweetened condensed milk until fully combined. Stir in melted white chocolate chips and vanilla extract until smooth and creamy.
Assemble the Lasagna: Spread the white chocolate cheesecake filling evenly over the graham cracker crust. Dollop spoonfuls of the blueberry compote over the filling. Use a knife or skewer to gently swirl the compote into the cheesecake mixture, creating a marbled effect.
Chill: Cover the baking dish and refrigerate for at least 4-6 hours, or preferably overnight, until firm.
Serve: Cut into squares and serve cold.