Chop the chicken into bite-sized pieces and set aside. Prepare all vegetables by peeling and slicing the carrots and chopping the celery. Mince the garlic and chop the herbs for garnishing.
In a large heavy-bottomed pot, heat the olive oil or butter over medium heat until shimmering and fragrant. Add the chopped onions, carrots, and celery, sautéing until they soften and release a sweet aroma, about 8 minutes. The vegetables should be tender but not mushy.
Add the minced garlic to the vegetables and cook for another minute, stirring until fragrant. Then, pour in the chicken broth and bring to a gentle simmer. While it heats, season with salt and pepper to taste.
Once the broth is simmering, add the chicken pieces to the pot. Cover and cook gently for about 10 minutes, or until the chicken is cooked through and tender. During this time, the flavors will meld and the broth will develop a rich aroma.
While the chicken cooks, separately boil a pot of salted water and cook the noodles until just al dente, following package instructions. Drain and set aside.
Remove the cooked chicken from the broth and shred or chop it into smaller pieces if desired. Return the chicken to the soup and stir in the lemon juice, adjusting to taste for brightness.
Add the cooked noodles into the soup, stirring gently to combine. Let everything simmer together for another 2 minutes to allow flavors to meld and noodles to absorb some broth.
Taste the soup and adjust the seasoning with more salt, pepper, or lemon juice as needed. Ladle the soup into bowls and garnish generously with chopped herbs.
Squeeze additional lemon over each serving if desired, and enjoy this bright, comforting bowl of chicken noodle soup.