In a large pot, bring 4 quarts of water to a boil. Plunge lobster into the the fast-boiling water for 8 to 10 minutes. Remove lobster, and place in ice-water bath immediately to stop the cooking process.
First, twist legs and tail from body. Using fish scissors, cut around the inside of the shell. Starting from the tail end, peel it back and pull out the meat. For the claws, but through the joints and open each section by cracking the ends. Ease the meat out of the shells. Reserve all the meat and head can be used for making the lobster stock.
For the sauce, heat the olive oil in a saucepan, and add red chili pepper and cumin seeds. Saute' until slightly brown. Add shallots, kaffir lime leaves, lemongrass, cilantro, and basil. Continue to cook for about 2 minutes. Add the lobster stock and simmer for 10 minutes. Pour in coconut milk, lemon juice, and heavy cream; cook for another 3 minutes. Remove from heat and whisk in the room-temperature butter. Add salt to taste. Strain the sauce through a fine strainer.
Warm 4 soup plates. Cut lobster meat into bite-size pieces, and arrange in the center of the plate. Carefully spoon the sauce around the lobster meat.
Garnish with the cilantro leaves and asparagus spears, and serve immediately.