Coat a 5-quart or larger slow cooker with nonstick spray.
Heat olive oil in a large pan over medium heat and sauté carrots, celery, and onion until softened, about 8-10 minutes.
Stir in minced garlic and cook for 1 minute.
Transfer the sautéed vegetables to the slow cooker.
Add the rinsed brown rice, chicken, salt, pepper, bay leaf, and fresh thyme to the slow cooker.
Pour in the chicken stock until ingredients are covered.

Cover and cook on Low for 5 to 6 hours, or on High for 2 1/2 to 3 1/2 hours, until the rice is tender and the chicken registers 165°F.

If the chicken finishes before the rice, remove it first so it does not overcook, then re-cover and continue until the rice is tender.

Remove chicken, shred with two forks, and return to the pot.
Stir in the fresh lemon juice and remove the bay leaf and thyme stems before serving.