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1. Preheat the oven to 375 degrees F. Line a 9x13-inch pan with foil so it hands over the edges. Spray the foil-lined pan with nonstick cooking spray.
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2. In the bowl of a stand mixer fitted with a paddle attachment, mix the flour, granulated sugar and salt at low speed to combine, about 5 seconds. With the machine on low, add 1 cup of the butter, 1 piece at a time, then continue mixing on low until the mixture resembles damp sand, 1 to 11/2 minutes. (If using a food processor, process the flour, granulated sugar, and salt until combined, about 5 seconds. Scatter the 1 cup of butter pieces over the flour mixture and pulse until the mixture resembles damp sand, about twenty 1-second pulses.)
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3. Measure 11/4 cups flour mixture into a medium bowl and set aside; distribute the remaining flour mixture evenly in the bottom of the prepared baking pan. Using your fingers or the bottom of a measuring cup, firmly press the mixture into an even layer to form the bottom crust. Bake until the edges begin to brown, 14 to 18 minutes.
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4. While the crust is baking, add brown sugar, oats, and nuts to the reserved flour mixture; toss to combine. Work in the remaining 2 tablespoons of butter by rubbing the mixture between your fingers until the butter is fully incorporated. Pinch the mixture with fingers to create hazelnut-sized clumps; set streusel aside.
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5. Combine preserves, raspberries, and lemon juice in a small bowl; mash with a fork until combined but some berry pieces remain.
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6. Spread the filling evenly over the hot crust; sprinkle the streusel topping evenly over the filling (do not press streusel into filling). Return the pan to the oven and bake until the topping is a deep goldne brown and the filling is bubbling, 22 to 25 minutes. Cool to room temperature on a wire rack, 1 to 2 hours; remove from the baking an by lifting the foil extensions. Cut into squares and serve. The bars can be stored in an airtight container at room temperature.
