Transfer thighs to a cutting board (shake rice that sticks back into pot). Let rest 5 minutes then cut chicken into small pieces.
Meanwhile let soup continue to simmer, covered, until rice is tender, about 8 to 12 minutes longer.
Remove soup from heat. Remove parmesan rind and bay leaves. Stir in chicken, parsley and lemon juice.
As soup rests it will thicken you can thin with remaining 1 cup chicken broth if desired. Serve with shredded parmesan cheese to taste.