The beets turn these traditional latkes into a modern and festive shade of red, while carrots add a note of sweetness.
In a medium bowl, combine onion, lemon juice, and eggs. Add flour, salt, and pepper, and stir until incorporated. Add carrots, beets, and potato, and toss until combined and evenly coated.
Fill a large skillet with about 1/2 inch oil. Place over medium heat until oil is almost smoking. (To test, drop a small bit of batter into the skillet; it should sizzle upon contact.)
Working in batches so as not to crowd skillet, carefully spoon about 2 tablespoons batter into oil for each latke. Lightly tamp down to flatten. Cook, turning once, until golden on each side, 2 to 3 minutes. Using a slotted spatula, transfer to a paper-towel-lined wire rack to drain. Repeat with remaining batter. Serve immediately with sour cream and applesauce.
Because beets are high in sugar, these latkes brown very quickly, so keep an eye on them.