How to Make It
Preheat oven to 450°F. Place oven rack in top third of oven.
Heat 2 teaspoons oil in a Dutch oven over medium-high. Add carrots and shallot; cook until softened, about 2 minutes. Add garlic; cook until fragrant, about 30 seconds. Stir in thyme and 1/2 teaspoon salt. Add lentils, stock, and 2 cups water. Bring to simmer, cover partially, and cook until al dente, checking occasionally and adding more water as needed to keep lentils covered, about 25 minutes. Drain, reserving 1/4 cup cooking liquid.
Heat remaining 2 teaspoons oil in a large cast-iron skillet over medium-high. Sprinkle chicken with pepper and remaining 1/4 teaspoon salt. Place chicken in pan, skin side down. Cook until slightly browned, about 3 minutes. Flip and cook until other side is browned, about 3 minutes. Move pan to oven. Bake at 450°F until chicken is done, about 20 minutes.
Whisk together yogurt and zest in a medium bowl. Set aside.
Spread 1/4 cup yogurt mixture onto each of 4 plates; top each with 3/4 cup lentil mixture. Top each serving with 1 chicken thigh, drizzle with 1 tablespoon reserved cooking liquid, and garnish with thyme.