Preheat oven to 250°F with rack in upper and lower thirds.
Place 1 or 2 cooling racks on top of a large rimmed sheet pan with metal cooling rack(s).
Peel carrots and coarsely shred in a food processor fitted with medium shredding disk (or coarsely grate into a bowl using large teardrop-shaped holes on a box grater).
Repeat with potatoes and onion.
Add lemon juice and toss to coat.
Transfer mixture to a kitchen towel (not terry cloth) and enclose in towel, then wring out as much liquid as possible.
Wipe bowl clean, then return vegetables to bowl and stir in flour, eggs, and 1 teaspoon salt until just combined.
Heat oil in a large 12-inch nonstick skillet over medium-high heat until it shimmers. Fill a 1/4-cup measure with latke mixture and carefully spoon it into skillet, then flatten lightly to a 3-inch diameter with a heatproof spatula.
Form 5 more latkes in skillet and fry until undersides are golden, 2 to 3 minutes. (If latkes brown too quickly, reduce heat.) Turn over and fry until golden on other side, about 3 minutes more.
Transfer to paper towels to drain briefly, then transfer to a metal rack set on sheet pan in oven to keep warm. Make more latkes in same manner.
Latkes can be kept warm in the oven for up to 1 hour.
