In a large pot, melt the ghee over medium heat and add the diced onion, celery, and carrot.
Sauté the vegetables for 5-7 minutes until they are soft and the onion is translucent.
Stir in the tomato paste, dried thyme, sea salt, and black pepper, cooking for 1 minute to release the aromatics.
Pour in the seafood stock and bring the mixture to a gentle simmer for 10 minutes.
Use an immersion blender to blend the soup until it is completely smooth and creamy.
In a small bowl, whisk the arrowroot powder into the coconut milk until dissolved, then pour it into the pot.
Add the cooked lobster meat to the pot and simmer for an additional 3-5 minutes until the lobster is heated through and the bisque has thickened slightly.
Ladle the bisque into bowls and garnish with finely chopped fresh chives before serving.