Pour 1 inch of water into a large stockpot or dutch oven and place over high heat. Once the water comes to a boil, place a steaming basket on top of the pot and place the lobster parts in the basket. Cover and steam for 3 minutes.
Remove the lobster from the basket and crack the shells to extract the meat. Kitchen shears and crackers are handy to have for this task. Once the meat is extracted, set the meat aside. Break the tail, claw, and body shells down into smaller pieces and set them aside as well. Pour the lobster steaming liquid into a bowl and set it aside as well.
Add the butter and olive oil to the now-empty pot and place over medium heat. Once the butter is frothy, add the shallots, carrots, celery, and a healthy pinch of salt. Sauté until the shallots are just translucent.
Add the garlic, ginger, lobster shells, and shrimp shells if using. Sauté until the shells turn bright red. Stir in the red curry paste and shrimp paste and sauté until fragrant, about 3-5 minutes more.
Deglaze the pot with vermouth and pour in the stock and lobster steaming liquid. Add the bay leaves and bring everything up to a boil before reducing to a simmer. Cover and let cook for 1 hour.
Strain the stock through a fine-mesh strainer, pressing the shells to release any excess juices. Return the stock to the pot and pour in the coconut milk and evaporated milk. Bring the soup back up to a simmer. Let cook for 10 minutes.
While the soup is simmering, cook the noodles according to the package's directions. Drain and rinse the noodles, then divide them among 4 bowls.
Toss the lobster meat into the simmering soup and add the lime juice. Take the pot off of the heat and stir until the meat firms up and cooks through in the hot soup. Ladle the soup and lobster meat over the noodles and garnish with beansprouts, cilantro, reserved celery leaves, and radish microgreens. Serve the soup immediately with lime wedges on the side.