Add the oil and butter to a large lidded pot or dutch oven over medium heat.
When the butter is melted, add the leeks, carrots, and celery to the pot. Cook, stirring often, until the vegetables are soft, 7 to 9 minutes.
Stir in the garlic, salt, and ground black pepper and continue cooking until fragrant, 1 to 2 minutes.
Pour in the broth, water, coconut milk, and rice and stir to mix (if using dairy not coconut, wait to add milk until after rice is cooked).
Bring to a boil, reduce heat to medium low, and cover the pot.
Simmer until the rice is cooked, 13 to 15 minutes, then remove the lid, salt to taste, and add the lemon juice.
Stir in the rotisserie chicken and chopped parsley and simmer on low until serving.
Ladle into bowls and top with additional parsley.
