Peel potato and coarsely grate into a bowl. Add lemon juice and toss to combine. Place potato on towel, then gather up corners to form a sack and twist tightly to wring out as much liquid as possible. Stir potato together with parsnips, flour, eggs, chives, salt, and pepper until combined well.
Heat oil in a 12-inch nonstick skillet over moderate heat until hot but not smoking. Fill a 1/4-cup measure three-fourths full with latke mixture and carefully spoon it into skillet, then flatten to 3 inches in diameter with a slotted spatula. Form 3 more latkes in skillet, then cook until golden, about 1 1/2 minutes on each side. Transfer latkes with spatula to paper towels to drain. Keep warm on a rack set in a shallow baking pan in oven. Make more latkes in same manner, in batches of 4, with remaining mixture.