Preheat your oven to 350°F (175°C) and grease an 8x8-inch baking dish or line it with parchment paper.
In a mixing bowl, combine the flour, rolled oats, brown sugar, baking powder, and salt. Pour in the melted butter and mix until crumbly.
Press this mixture evenly into the bottom of the prepared baking dish to form the crust.
In another bowl, whisk together the granulated sugar, eggs, vanilla extract, and lemon juice until smooth.
Gently fold in the blackberries and chopped pistachios.
Pour this mixture over the crust in the baking dish.
Bake for 25-30 minutes, or until the top is set and lightly golden.
Allow the bars to cool in the pan for at least 15 minutes before slicing into squares.