In a large pot, heat 4 tbsp of the oil over medium heat. Sweat celery, onion and garlic with a pinch of salt.
Add the crushed tomatoes and dry basil. Season the tomatoes with salt and cook for another minute. Add wine and let simmer for 10 minutes.
Add lobster stock and continue to simmer for 30 minutes, and then lower the heat.
In a small saucepan, melt the butter and remaining 1 tbsp of oil. Add the flour and cook for a minute, stiring. Gradually whisk in the milk, continuously stirring. Once the mixture begins to thicken, add it to the soup.
Add raw lobster meat to the soup and let cook just through, about 2 minutes.
Transfer half of the soup to a blender. Blend until smooth and return to the soup pot. Check for seasoning.
Grill slices of bread and place one slice at the bottom of each individual bowl. Pour soup into the bowls, garnish with a sprinkling of red pepper flakes, torn basil and chopped chives. Add a drizzle of your best quality extra-virgin olive oil, and serve.