IN A LARGE MIXING BOWL, BEAT SUGAR, POWDER SUGAR, BUTTER AND OIL UNTIL LIGHT AND FLUFFY. ADD LEMON PEEL, LEMON JUICE AND EGG, BLENDING WELL.
STIR IN FLOUR, CREAM OF TARTAR, BAKING SODA AND SALT, BLENDING WELL. COVER WITH PLASTIC WRAP AND REFRIGERATE FOR 1 HOUR FOR EASY HANDLING.
PREHEAT OVEN TO 350°
SHAPE DOUGH INTO 1" BALLS, ROLL IN SUGAR. PLACE 2" APART ON UNGREASED COOKIE SHEETS. BAKE FOR 7 TO 12 MINUTES OR UNTIL SET. IMMEDIATELY REMOVE FROM COOKIE SHEET TO A WIRE RACK.