Heat the avocado oil in a large pot or Dutch oven over medium heat. Season the chicken thighs lightly with salt and pepper, then add them to the pot. Sear and cook through until golden on the outside and fully cooked. Remove from the pot and set aside.
In a separate pot, cook the rice according to package directions. Fluff and set aside for serving.
In the same pot used for the add more oil if needed then add chicken, add the onion, celery, and carrots. Cook for a few minutes, stirring occasionally, until they begin to soften. Add the garlic and ginger and cook for another minute until fragrant.
Stir in the Italian seasoning, then pour in the chicken broth and add the Better Than Bouillon and bay leaves. Bring everything to a gentle boil.
While the soup is coming together, chop or shred the cooked chicken into bite-sized pieces.
Once the broth is simmering, return the chicken to the pot and let everything cook together for about 10–15 minutes so the flavors can develop. Season with salt and pepper to taste.
Turn off the heat, then stir in the fresh lemon juice.
To serve, add cooked rice to each bowl and ladle the soup over the top. Finish with fresh parsley if desired.