Use a peeler to peel wide strips of carrots. You may need to discard several strips before the strips become wide. They will get wider as you go and it's OK if they aren't all the exact same width and length. There should be about 30 strips.
In a small saucepan on high heat, bring lemon juice, water, and sugar to a boil, stirring until sugar has dissolved.
Add carrot strips and reduce heat to medium-low. Simmer for 15 minutes.
Remove from the heat and strain out liquid. (The liquid can be discarded, but I like to save it to sweeten drinks. It is also really good to use as part of a sauce for a lemony chicken dish.)
Let stand until carrot strips are comfortable to the touch.
Preheat oven to 225 F with a rack in the middle.
Arrange candied carrot slices flat in a single layer on a parchment- or silicone mat-lined baking sheet.
Bake until dry but not brittle, about 30 minutes. (Leave oven on.)
Working quickly, wind carrot strips, one at a time, in a loose spiral around a chopstick. Place the chopstick with the carrot still wrapped around it back on the baking sheet, seam side down.
Return the baking sheet to the oven for up to 45 minutes. Check on the curls periodically starting at 20 minutes to make sure that they aren't browning. If you see signs of this, pull them early. Cook rates vary based on the thickness of the carrot strips.
Remove the curls from the oven, leaving them on the chopsticks to cool.
If curls are crisp, slip them off the chopsticks. If they are still a little soft, return to the oven for another 20 minutes.
Carrot curls can be made up to five days in advance. Store in a loosely-covered container at room temperature. When ready to use, recrisp if necessary in a 250 F oven for 10 minutes. Warning: Don't put them on your cake until just before serving or the curls will get soggy.
Adapted from Epicurious (they got it from the December 2007 issue of Gourmet).