Warm the olive oil in a large pot over medium heat.
Add onion, carrots, and celery with half the salt. Cook, stirring, until softened, 5–7 minutes.
Stir in garlic and thyme. Cook until fragrant, about 30 seconds.
Pour in the broth and bring to a gentle boil.
Stir in rice. Reduce heat to a simmer and cook until tender, 15–18 minutes.
Add the shredded turkey and peas. Simmer until heated through, 3–5 minutes.
Finish with pepper, remaining salt, lemon juice, and parsley. Adjust seasoning to taste.
Let the soup rest 5 minutes to thicken slightly, then ladle into bowls and serve.