Bring a large pot of salted water to a rolling boil. Carefully add the potatoes. Return to the boil and continue cooking until the potatoes are tender, 10 minutes or so. Drain, then spread in a single layer on a baking sheet to quickly cool.
1. To a blender or food processor, add the anchovies and their oil, olive oil, mustard, hot sauce, lemon zest and juice, and garlic. Purée until smooth.
2. In a large bowl, combine the cooled potatoes, lobster, carrots, celery, parsley, and dill. Add the dressing and thoroughly toss.