To make crust: Preheat oven to 350 °F. Coat an 8-by-12-inch or 7-by-11-inch baking pan with cooking spray.
Stir together flour, baking powder, baking soda and salt in a small bowl. Beat together 1/2 cup sugar, butter, oil, egg white and 1 teaspoon vanilla in a mixing bowl with an electric mixer until smooth. Stir in the dry ingredients until blended and crumbly. Press the dough into the prepared baking pan in an even layer. Bake the crust until it is puffed all over and browned around the edges, 15 to 20 minutes.
To make raspberry and cream layers: While the bars are baking, stir together 1/4 cup sugar and cornstarch in a saucepan. Add raspberries and toss. Stir over medium heat until the mixture is simmering and thickened. When the crust is baked, spread the warm raspberry mixture in an even layer over the crust.
Whisk together sweetened condensed milk, yogurt, egg, cornstarch, lemon juice, lemon zest and 1 teaspoon vanilla in a bowl until smooth; pour over the raspberry layer, tilting the pan to spread it evenly. Drag a fork through the cream layer down into the raspberry layer below to create a marbled effect. Bake until the filling is puffed and set, 25 to 30 minutes. Let cool completely in the pan on a wire rack. Cut into squares.
Make Ahead Tip: Cover and refrigerate for up to 2 days.