Prepare the Pan and Preheat the Oven
Preheat your oven to 350°F (177°C) and position the rack in the center.
Line an 8×8-inch baking pan with two overlapping sheets of parchment paper, leaving an overhang on all sides for easy removal.
Melt the Butter
Cut the butter into pieces and place it in a microwave-safe bowl. Melt the butter in 20-second intervals, stirring after each interval until fully melted. (You can also melt the butter on the stovetop.)
Make the Crumb Mixture
To the melted butter, stir in the brown sugar, baking powder, and 1/2 teaspoon of kosher salt.
Add the oats and flour, mixing with a spatula until the mixture is well combined and crumbly.
Reserve 1 cup of the crumb mixture for the topping and set aside.
Form the Base Layer
Press the remaining crumb mixture firmly and evenly into the prepared baking pan.
Bake for 12–14 minutes, or until fragrant and lightly golden. Remove from the oven and let cool slightly.
Prepare the Lemon Filling
Finely zest the lemons to yield about 2 tablespoons of zest. Juice the lemons to make 1/2 cup of fresh lemon juice.
In the same bowl used for the crumb mixture, whisk together the lemon zest, lemon juice, sweetened condensed milk, and the remaining 1/4 teaspoon of kosher salt until smooth.
Assemble and Bake the Bars
Pour the lemon filling evenly over the baked crust.
Sprinkle the reserved 1 cup of crumb mixture evenly over the top.
Bake for 22–24 minutes, or until the edges are set and lightly browned.
Cool and Slice
Place the pan on a wire rack to cool completely, about 1 1/2 hours. For a firmer texture, refrigerate for an additional 30 minutes after cooling.
Using the parchment paper overhang, lift the bars out of the pan and transfer them to a cutting board.
Slice into 12 equal pieces and serve.