Preheat oven to 325^. Line cookie sheets with parchment paper; set aside.
Combine flour, baking powder, salt and baking soda. In a large mixing bowl cream butter on medium to high speed for 30 seconds. Add sugar and lemon zest. Beat until well combined. Add eggs one at a time blending well after each addition. Add lemon juice and beat until incorporated.
Gradually add flour mixture until combined. Stir in walnuts. Divide dough into 3 portions. On lightly floured surface shape each portion (I usually do this straight on the parchment paper lined cookie sheet) into a 10" roll about 1 1/2" wide. Press each log until 2" wide. Brush with egg white and sprinkle with coarse sugar.
Chill cookie sheet(s) for 15 minutes. Bake 25-30 minutes. Remove from oven and cool on sheets for 45 minutes.
Preheat (or reduce) oven to 300^. Cut each cooled log with serrated knife diagonally into 1/2" slices and place cut side down on cookie sheets. Bake 7 minutes; turn over and bake an additional 5-6 minutes. Remove to wire racks to cool completely.
Yield: 4-5 dozen