Heat the olive oil in a large pot over medium heat. Add the onion, carrots and celery and cook, stirring occasionally, until softened, 6 to 8 minutes. Add the garlic and thyme and cook 1 minute more.
Pour in the chicken broth and add the chicken breasts. Bring to a boil, then lower the heat and simmer gently until the chicken is cooked through and reaches 165 °F in the center, 12 to 15 minutes.
Transfer the chicken to a cutting board and shred it with two forks.
Add the egg noodles to the simmering broth and cook until tender, 6 to 8 minutes.
Return the shredded chicken to the pot. Stir in the dill and lemon juice, then season with salt and pepper to taste. Ladle into bowls and top with extra dill.