Rinse quinoa well and cook according to package instructions. Spread on a rimmed baking sheet to cool.
Meanwhile, whisk lemon juice with oil, salt, and sugar in a large bowl. Add carrots and toss to coat.
Mix in cooled quinoa and chickpeas, then transfer salad to a lidded container.
*Using a hand-held slicer makes the slicing go faster.
Make ahead: Up to 2 days, covered and chilled.