Make the applesauce: Cut the apples into 1-inch pieces. Remove 3 wide strips zest from the lemon with a vegetable peeler; transfer to a saucepan and squeeze in the lemon juice. Add the apples and cinnamon stick, cover and cook over medium heat until soft, 15 to 20 minutes. Uncover and increase the heat to medium high. Continue to cook, mashing and stirring the apples, until they thicken, 10 to 15 minutes. Remove the cinnamon stick, then pass the apples through a food mill or puree in a food processor. Set aside until ready to serve.
Meanwhile, make the latkes: Grate the potatoes, parsnips and onion using the medium grater attachment of a food processor or the large holes of a box grater. Squeeze the mixture by the handful over the sink to remove any excess liquid. Mix with the garlic, eggs, parsley and chives in a large bowl, then add the flour and 1/2 teaspoon each salt and pepper. Shape into 12 thin patties, squeezing to remove any remaining liquid as you form each one; lay on a sheet of parchment.
Heat 1/4 inch of peanut oil in a large skillet over medium-high heat. Fry the latkes in batches until golden brown, 4 to 5 minutes per side. Drain on paper towels and season with salt while hot. Serve with the cinnamon applesauce.