Preheat oven to 350°F.Line an 8x8-inch baking pan with parchment paper, leaving a little overhang on the sides to make the bars easier to lift out later.
In a food processor, combine flour, powdered sugar, salt, and cold butter. Pulse until the mixture looks like coarse crumbs and begins to hold together when pressed.Press the crust mixture evenly into the bottom of the prepared pan.Bake for 16–18 minutes, or until lightly golden around the edges.
While the crust bakes, add strawberries, sugar, and lemon juice to a small blender or food processor.Blend until smooth.For a smoother filling, strain the puree through a fine mesh strainer to remove seeds. This step is optional.
In a medium bowl, whisk together eggs, sugar, lemon juice, lemon zest, flour, and salt until smooth.Stir in the strawberry puree.
Pour the strawberry lemon filling over the warm baked crust.Use a toothpick or butter knife to gently swirl the filling for a marbled strawberry lemonade look, if desired.
Bake for 20–24 minutes, or until the edges are set and the center has only a slight jiggle.Do not overbake. The bars will continue to set as they cool.
Let the bars cool completely at room temperature. Transfer the pan to the refrigerator and chill for at least 2 hours before slicing.
Lift the chilled bars from the pan using the parchment paper.Dust with powdered sugar, then top with fresh strawberry slices and lemon zest if desired.Slice into squares and serve chilled.