Fill a large pot with salted water and bring it to a rolling boil. Add the lobsters and cook them for about 8 to 10 minutes until done. Take them out, let them cool just enough to handle, then remove the meat and set aside the shells. Chop the lobster meat finely and chill it in the fridge.

Heat the olive oil and butter together in a big pot over medium heat. Add the chopped onion, carrots, and celery, then cook them gently for 8 to 10 minutes until they become soft. Add the minced garlic and cook for an additional 30 seconds to release its aroma.

Stir in the tomato paste and let it cook for 2 to 3 minutes until it darkens slightly. Sprinkle in the flour and cook for another 1 to 2 minutes while stirring continuously to form a flavorful base.

Pour in the mixture of seafood stock and lemon juice, making sure to scrape the bottom of the pot to loosen up all browned bits. Let it simmer gently for 2 to 3 minutes to combine the flavors.

Add the reserved lobster shells along with the seafood stock, paprika, bay leaf, and thyme into the pot. Bring everything to a gentle boil, then lower the heat to maintain a simmer for 30 to 40 minutes, allowing the flavors to develop deeply.

Take out the bay leaf and use an immersion blender to puree the soup until smooth. Then push the bisque through a fine mesh sieve into a clean pot to remove any solids for a silky texture.

Pour in the heavy cream and the chopped lobster meat, stirring gently. Let the bisque heat through over low heat for 5 to 7 minutes. Season it with salt, freshly ground black pepper, and a pinch of cayenne pepper if desired.

Serve the bisque hot by ladling it into warmed bowls. Garnish with your preferred herbs or toppings and enjoy a comforting, elegant meal.