Fill a large stockpot 3/4 full with salted water and bring to a boil. Plunge the lobsters headfirst into the boiling water and cook, covered, for 6 minutes. Transfer with tongs to a large bowl filled with ice water to cool, reserving the cooking liquid. When the lobsters are cool enough to handle, crack the shells over a bowl to reserve any juices, and remove the meat from the tail and claws. Reserve the shells. Coarsely chop the meat and set aside. Discard the sacs.

Cut the kernels from the corn and reserve. Reserve the corncobs for the stock.

To make the lobster stock, in a large, heavy pot, heat the oil over medium-high heat. Add the shells and cook, stirring, for 10 minutes. Add the roughly chopped carrots, celery, and onions, smashed garlic, bay leaves, 2 sprigs of the thyme, the peppercorns, and 1 teaspoon of the salt, and cook, stirring, for 3 minutes. Add 2 quarts of water, the corncobs, and any reserved lobster juices, and bring to a boil, skimming with a slotted spoon to remove any foam that rises to the surface. Reduce the heat to medium-low and simmer uncovered until reduced to 4 cups, 1 to 1 1/2 hours.

Remove the stock from the heat and strain through a fine mesh strainer. Discard the solids and reserve the stock.

In a large pot, cook the bacon over medium-high heat until golden brown and the fat is rendered, about 5 minutes. Remove with a slotted spoon and drain on paper towels. Discard all but 1 tablespoon of the bacon fat. Melt the butter with the bacon fat over medium-high heat. Add the onions, celery, garlic, cayenne, remaining sprig of thyme, and 1/2 teaspoon salt and cook, stirring, until the vegetables are soft, 4 minutes. Add the flour to make a roux. Cook for a few minutes, until the roux mixture bubbles. Add the strained stock, reserved corn, and potatoes and bring to a boil. (If the stock does not cover the potatoes, add enough water to cover.) Reduce the heat, replace the lid ajar, and simmer, stirring occasionally, until the potatoes are tender, about 20 minutes.

Remove the pot from the heat and stir in the reserved lobster meat, cooked bacon, cream, and parsley. Return to the heat and cook at a bare simmer until the lobster is cooked through and the chowder is creamy. Finish with butter. Remove from the heat and discard the thyme sprig. Adjust the seasoning to taste.

Ladle into bowls and garnish with the chopped chives. Serve hot.