Heat oven to 325°F. In large bowl, combine butter and sugar; beat until light and fluffy.
Lightly spoon flour into measuring cup; level off. Add flour, ginger and lemon peel; mix well. Shape dough into ball; divide into 4 pieces. On ungreased cookie sheets, flatten each piece to 6-inch round; press edges to smooth.
Bake at 325°F. for 15 to 25 minutes or until edges are light golden brown. Cool 5 minutes. Cut each round into 8 wedges; pierce surface with fork if desired. Cool on cookie sheet for 15 minutes or until completely cooled.
In small bowl, combine powdered sugar and enough lemon juice for desired drizzling consistency; blend until smooth. Place mixture in small resealable food storage plastic bag; seal bag. Cut off small corner of bag. Squeeze glaze onto cooled cookies.