Preheat oven to 350 degrees.
Whisk the egg whites until frothy. Add the sugar and whisk until stiff but not dry.
Fold in the confectioners' sugar, coconut and lemon zest. Place in a double boiler or in a metal bowl over barely simmering water. Stir constantly until the mixture is hot.
Stir in the flour.
Line two baking sheets with parchment paper. Using heaping teaspoons full of the batter; spoon the cookies onto the baking sheets, placing them 2 inches apart.
Bake until the cookies are golden brown, about 15 minutes. Transfer to a rack to cool.