Preheat oven to 350 degrees F (175 degrees C). In a medium bowl, mix together 1 1/2 cups flour, 1/4 cup sugar and 1/2 cup butter until the mixture is mealy. Press into the bottom of an ungreased 9x9 inch pan.
Bake for 20 minutes in the preheated oven, or until golden. In a medium bowl, beat eggs until light, and stir in the 3 tablespoons of lemon juice. Combine 1 cup sugar, 2 tablespoons flour, baking powder and salt (if desired); whisk into the eggs. Stir in the coconut. Pour over the baked crust and spread evenly.
Bake for 25 to 30 minutes in the preheated oven, until center is set and bars are golden. Cool and frost. To make the frosting: In a small bowl, stir together the confectioners' sugar and 2 tablespoons butter. Mix in the lemon juice 1 teaspoon at a time as needed for desired spreading consistency. Spread over cooled bars.