Place the whole chicken in a large (7-quart) Dutch oven with the onion, carrots, celery, bay leaves and peppercorns. Cover with water and bring to a boil over medium-high heat. Lower the heat to medium-low and simmer, covered until the chicken is cooked through, about 45 minutes.
Remove the chicken to a cutting board and let cool. Shred the chicken and set aside. Add the bones back to the pot and continue to cook for an additional hour, uncovered. Strain the broth into a large mixing bowl and discard the bones, vegetables and aromatics. Season the broth to taste with salt.
Return the strained broth to the Dutch oven over medium heat. Add the orzo and cook until al dente, about 7 minutes. Set aside 2 cups of the broth. Add ¾ pound of the shredded chicken to the soup (reserve the rest for another use).
Add the eggs to a medium bowl and whisk until frothy and the eggs fall in ribbons. Slowly add the lemon juice while continuing to whisk.
Temper the eggs by slowly adding the reserved chicken broth in a thin stream. Add the egg/ broth mixture to the pot, stirring to combine. Cook until the soup thickens slightly, about 5 minutes. Do not let the mixture come back to a boil.
Ladle into warmed soup bowls. Garnish with lemon slices, cracked black pepper and dill and serve hot.