Beat together butter and sugar in small bowl with electric mixer until light and fluffy. Beat in egg, lemon peel, vanilla and salt. Gradually beat in flour until thoroughly incorporated. Add water, a few drops at a time, only until dough starts to come away from side of bowl. Wrap dough in plastic wrap. Refrigerate until firm, about 2 hours.
Preheat oven to 350F. Lightly grease 4 cookie sheets. On lightly floured surface, roll out dough to 1/8