Heat the olive oil in a large pot over medium heat. Add the chopped leeks, diced onion, celery, and minced garlic. Sauté for about 5 minutes until softened.
Add the cubed potatoes, vegetable broth, dried thyme, dried rosemary, bay leaf, salt, and pepper. Bring the mixture to a boil, then reduce the heat and simmer for about 20 minutes, or until the potatoes are fork-tender.
Remove the bay leaf. Stir in the lemon juice and coconut milk. Using an immersion blender, blend most of the soup until smooth, leaving some potato pieces for texture. Adjust salt and pepper to taste.
If needed, add more broth or coconut milk to thin the soup. Garnish with chopped fresh chives and serve warm.
