Preheat your oven to 350°F (175°C). Grease a 9x9 inch baking pan and set aside.
In a large mixing bowl, combine the flour, rolled oats, brown sugar, granulated sugar, baking powder, and salt. Mix well to combine.
Pour in the melted butter and stir until everything is moistened and crumbly. Reserve about 1 cup of the mixture for topping.
Press the remaining crumb mixture evenly into the bottom of the prepared pan to form a crust. Bake for 15 minutes, or until lightly golden.
While the crust is baking, prepare the lemon raspberry filling. In a separate bowl, whisk together the eggs, granulated sugar, lemon zest, and lemon juice until combined.
Gently fold in the fresh raspberries until just incorporated.
Pour the raspberry filling over the pre-baked crust and spread evenly.
Sprinkle the reserved crumb topping evenly over the raspberry filling.
Bake for an additional 25-30 minutes, or until the topping is lightly golden and the filling is set.
Allow to cool completely in the pan before slicing into squares. Dust with powdered sugar before serving.
Notes
Serve the crumb bars on a decorative plate, garnished with additional fresh raspberries and a sprinkle of lemon zest for an appealing pop of color.