Heat olive oil and butter in a large pot over medium heat.
Add diced onion, sliced carrots, and sliced celery; sauté for 4 to 5 minutes until softened.
Add minced garlic and cook for about 30 seconds until fragrant.
Pour in turkey or chicken broth and bring the mixture to a gentle boil.
Stir in uncooked rice, salt, pepper, dried thyme, dried oregano, and bay leaf.
Reduce heat to medium-low and simmer for 15 to 18 minutes until the rice is tender.
Add cooked turkey and optional peas or corn; simmer for an additional 5 minutes until heated through.
Remove the bay leaf from the soup.
Stir in lemon juice if using and adjust seasoning to taste.
Ladle soup into bowls and garnish with chopped fresh parsley or dill.
Serve warm alongside crusty bread or crackers.