In a large skillet or sauce pan, combine coconut milk, cooked butternut squash, sauces, half of the lime juice, and spices. Bring liquid to a simmer for about 5-7 minutes, then transfer to a blender or food processor, add in curry paste, and blend until smooth. Return to a skillet and heat on a low temperature for 5-10 minutes.
In medium-sized skilled, heat oil on medium heat. When oil is hot, add in lobster, remaining lime juice, and salt and pepper to taste. Cook for about 3-4 minutes, or until lobster is tender (but not rubbery).
Remove from heat, drain some of the excess liquid, and add to the soup. Garnish with fresh basil and cracked pepper and serve warm.
Optional to serve with cooked Black Forbidden Rice.