Preheat oven to 325 degrees. Butter an 8-inch square baking pan, and set aside.
In a medium saucepan, combine cranberries and 2 cups water; bring to a boil. Reduce heat to medium, and cook, stirring occasionally, until water has been absorbed, about 25 minutes.
Transfer cranberry mixture to bowl of a food processor; chop coarsely. Transfer to a bowl, and set aside.
In bowl of an electric mixer fitted with the paddle attachment, combine confectioners' sugar and 3/4 cup flour. Add butter, beating on low speed until mixture forms pea-size pieces. Press batter into baking pan.
Bake until golden, about 20 minutes. Transfer to a wire rack to cool.
Beat eggs and granulated sugar until smooth. Add lemon juice; beat to combine. Add remaining 1/4 cup flour, and beat to combine; set lemon mixture aside.
Reduce oven temperature to 300 degrees. Spread cranberry mixture over cooked crust. Pour lemon mixture over the cranberry mixture. Bake until set, about 40 minutes. Transfer to a wire rack to cool, 40 minutes. Chill 4 hours. To serve, cut into squares, and dust with confectioners' sugar.