In a large pot or Dutch oven, melt butter over medium heat. Add onion, celery, and bell pepper and cook until softened, about 5-7 minutes.
Stir in flour and cook for 1 minute.
Gradually whisk in chicken broth until smooth.
Add potatoes, thyme, black pepper, and cayenne pepper. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until potatoes are tender.
Add conch and simmer for another 10-15 minutes, or until conch is tender.
Stir in heavy cream and lemon juice. Heat through, but do not boil.
Serve hot.