Preheat the oven to 350°F (175°C). In a mixing bowl, combine flour, powdered sugar, and salt. Mix well, then add softened butter and blend until it resembles coarse crumbs. Press into the bottom of a greased 8x8-inch baking dish and bake for 15 minutes until lightly golden.

In a separate bowl, whisk together eggs, granulated sugar, lemon juice, lemon zest, and baking powder until smooth. Gently fold in cranberries.

Pour the cranberry mixture over the baked crust and spread evenly. Bake for an additional 20-25 minutes until the filling is set and slightly golden around the edges.

Let the bars cool completely in the pan on a wire rack. Dust with powdered sugar before cutting into squares.