Heat oil in a skillet over medium heat. Add chicken; cook until juices run clear, 5 minutes on each side. Transfer chicken to a plate; set aside.

Add onion to the skillet; cook until tender, 5 minutes. Stir in carrot and garlic, then stir in broth and lentils; season with salt. Bring to a boil, cover, reduce heat to low, and simmer 20 minutes.

Return chicken to skillet. Cover, and continue cooking 20 minutes more. If mixture becomes too dry, add a little water just to moisten.

Stir in tomato sauce; season with rosemary and basil. Continue cooking until lentils tender, 10 minutes more. Stir in lemon juice. Serve warm.