Melt shortening in a large Dutch oven. Sauté chicken in shortening until brown on all sides. Add 6 cups water, and bring to a boil. Cover and simmer 1 hour or until chicken is tender. Remove chicken from broth; cool. Bone chicken, and chop meat.
Bring broth to a boil; stir in chopped chicken, onion, potatoes, carrots, lima beans, salt, and pepper; simmer, uncovered, 30 minutes.
Combine flour and remaining water, stirring until smooth. Stir flour mixture into stew; cook, stirring constantly, until thickened.