Process basil and 1/4 cup sugar in a food processor until blended.
Beat butter at medium speed with an electric mixer until creamy; gradually add remaining 1 1/2 cups sugar, beating well. Add lemon juice and egg, beating until blended. Gradually add flour and basil mixture, beating until blended.
Shape dough into 1-inch balls, and place 2 inches apart on lightly greased baking sheets. Flatten balls slightly with bottom of a glass dipped in sugar.
Bake at 350° for 8 to 10 minutes or until lightly browned. Remove to wire racks to cool completely.
*Regular Italian ('Genovese') basil may be substituted for lemon basil.