In saucepan, bring lemon juice, milk, 5 Tbs. olive oil, salt and lemon peel to a boil.
With wooden spoon, vigorously stir in all the flour until dough forms a ball. Beat in eggs, one at a time, incorporating each completely. Set aside.
Pour olive oil into large skillet to reach depth of 2 inches. Heat to 375 degrees F. Pinch off 1-inch pieces of dough and carefully lower into hot oil using slotted spoon. Fry until deep golden, about 1 minute. Transfer to paper towels to drain. Dust with sugar. Serve hot.