In a large pot, melt the ghee over medium heat.
Add the diced yellow onion, celery, and carrot, sautéing until the vegetables are softened and fragrant.
Stir in the minced garlic, tomato paste, and arrowroot powder, cooking for one minute to toast the paste.
Pour in the dry sherry to deglaze the pan, scraping up any browned bits from the bottom.
Add the seafood stock, sea salt, black pepper, and fresh thyme, then bring the mixture to a gentle simmer for 15 minutes.
Use an immersion blender to puree the soup base until completely smooth and velvety.
Stir in the full-fat coconut milk and the cooked lobster meat, heating through for 3-5 minutes without boiling.
Ladle the bisque into bowls and serve immediately while hot.