Heat the olive oil in a large stockpot over medium heat. Add the onion, carrots, celery, 1 teaspoon of salt, and ½ teaspoon of pepper. Cook, stirring occasionally, until softened, about 10 minutes.

Add the garlic and thyme. Cook, stirring constantly, until fragrant, about 1 minute. Add the chicken, the bay leaves and the remaining salt and pepper.

Add the water and rice, and bring everything to a boil over medium-high heat. Reduce the heat to medium-low and simmer, covered, until the chicken is cooked through, about 25 minutes.

Transfer the cooked chicken to a cutting board and chop into ½-inch pieces. Return the chopped chicken to the soup and remove the soup from the heat. Stir in the lemon juice and parsley.