Preheat oven to 350 degrees. Line a 13x9-inch pan with foil (allow some foil to hang over the edges) and lightly grease the foil. Set aside.
In a small saucepan, combine the ingredients for the raspberry sauce. Cook over medium heat, stirring frequently, until the mixture is thick and bubbly. Mash any whole berries with the back of a spoon until the mixture reaches your desired consistency. Turn heat to low to keep the mixture warm.
Combine the crust ingredients in a food processor. Pulse until the mixture resembles coarse sand. Pour the crust mixture into the prepared pan; press into the bottom and about 1/2 inch up the side of the pan. Crust will appear very crumbly - this is ok, it will come together in the oven. Bake for about 8 minutes, or until lightly golden.
While crust is baking, whisk together the ingredients for the lemon filling until completely blended and incorporated.
Remove the baked crust from the oven and immediately spread the warm raspberry sauce evenly over the bottom. Pour the lemon filling over the raspberry sauce - it will naturally mix and swirl with the raspberry sauce. Return to oven and bake for 20-25 minutes, until browned around the edges and no longer jiggly in the center.
Allow bars to cool completely in the pan. Use the foil to lift the bars from the pan; cut into squares and dust with powdered sugar to serve. To store, place in an airtight container with waxed paper or parchment paper separating the layers. Bars will last, in an airtight container, in the refrigerator for up to 4 days.
Notes
Makes 13x9-inch panLemon filling from the Joy the Baker Cookbook. Crust from my recipe for Caramel Pecan Bars.