Bring a pot of salted water to a boil. When hot, add capellini noodles and cook until al dente, about 3 minutes. Drain and rinse under cold water.
In a large soup pot over medium heat, add curry paste, ginger, and lemongrass. Cook until fragrant, about 1 minute; stir contents frequently to make sure nothing sticks to the pot. Add the coconut milk and continue to cook; make sure the broth does not boil. Then, add the fish sauce, brown sugar, and chicken stock and cook for 10 more minutes. Mix in coriander leaves.
Meanwhile, prepare the lobster tails. Dampen 3 bamboo skewers and skewer them in the bottom of the lobster tail, so they do not curl. Add lobster tails to the broth to poach for about 5 to 7 minutes, or until it reaches 140F with an instant-read thermometer. Immediately remove the lobster tails and assemble the bowl.
Start by dividing the capellini noodles among 3 bowls. Then, top with lobster tails and ladle spoons of poaching broth on top. Add a squeeze of lime juice; garnish with lime zest and leftover cilantro sprigs.