Sift flour again, with sugar, baking powder and salt.
In a large bowl use an electric mixer to beat eggs, milk, 1 teaspoon oil, vanilla and lemon zest. Gradually add flour mixture, beating until smooth. Fold diced apples into batter.
Fill a Dutch oven or stockpot with vegetable oil to at least 2 inches deep. Place over high heat until oil reaches 360 degrees (use a deep-fat thermometer to assure accuracy), then reduce heat to medium. Drop batter by generous tablespoonfuls into the pot, cooking three or four fritters at a time, and fry until deep golden brown, about 3 to 4 minutes. Drain on a rack, sprinkle with powered sugar, if desired, and serve immediately with warm caramel sauce.