In a large bowl, sift together flour, salt, and baking powder. Set aside.
Use an electric mixer to cream butter and sugar until light and fluffy. Beat in eggs one at a time. Add flour mixture, and mix on low speed until thoroughly combined. Stir in vanilla or lemon juice and zest.
Form dough into four balls and flatten into disks, wrap each disk in plastic wrap; chill for about 30 minutes.
Preheat oven to 325º F. On a floured surface, roll dough to ¼ inch thick. Cut into desired shapes. (Dough scraps may be chilled and re-rolled once to make additional cookies.) Transfer to ungreased baking sheets; refrigerate until firm, 15 minutes.
Bake until edges just start to brown, 10 to 12 minutes. Cool on wire racks.
Cookies may be stored at room temperature in an airtight container for up to 2 weeks, and they freeze great!