Place the onion, carrots, celery, Worcestershire, 6 cups water, and chicken (breast-side up) in a 6- to 8- quart pressure cooker. Season with 1 teaspoon salt and ½ teaspoon pepper.
Secure the lid and bring to high pressure over medium-high heat. Reduce temperature and cook over medium-low heat for about 30 minutes. Release the pressure and remove the lid. The chicken should be cooked through.
Transfer the chicken to a bowl and let cool. When the chicken is cool enough to handle, shred the meat (discard the bones and skin).
Meanwhile, skim any excess fat from the soup. Add 2 cups water to the pot and bring to a boil. Add the noodles and cook until tender, 4 to 6 minutes. Stir in the reserved chicken, peas, dill, and lemon juice. Simmer until warmed through, 2 to 4 minutes.