Preheat oven to 350?F. Spray 8x8-inch pan with nonstick spray.
Prepare base: In a medium bowl, beat butter and sugar until creamy. Stir in flour and salt until well combined and crumbly. Press into the bottom of prepared pan. Bake about 12 minutes until just barely golden around the edges.
Prepare topping: In the same bowl (no need to wash it) combine sugar, flour, baking powder and salt. Add egg and egg white, lemon juice and stir until well-blended and smooth.
Smooth cranberries and coconut evenly over the base. Pour lemon filling over top. Bake 40 to 45 minutes until golden and set. Cool completely in the pan on a wire rack.
Sprinkle with powdered sugar, if using, before cutting into squares.