Sauté the vegetables: Melt the butter with the olive oil in a large pot over medium heat. Add the onion, carrots, and celery and cook for 6 to 7 minutes, stirring often, until the onion softens. Stir in the garlic and cook for 30 seconds.
Build the broth: Pour in the chicken broth, then add the bouillon paste, thyme, bay leaf, salt, and pepper. Stir until the bouillon dissolves.
Poach the chicken: Add the whole chicken to the pot and bring to a boil. Reduce to a gentle simmer, cover, and cook for 18 to 20 minutes, until the chicken reaches 165°F.
Cut the chicken: Transfer the chicken to a cutting board, rest for 5 minutes, then cut or pull into bite-size pieces.
Cook the noodles: Return the soup to a boil, add the egg noodles, and cook for 6 to 8 minutes, until tender.
Finish and serve: Remove the bay leaf. Stir in the chicken, parsley, and lemon juice. Taste, adjust the salt and pepper, and serve hot.