In a tall stockpot, bring 5 cups water, the vodka, sugar, and 1 tsp. salt to a boil over medium-high heat. Meanwhile, kill the lobsters.
Add the lobsters to the pot and steam, covered, until they’re bright red and a small leg easily pulls away from the body, about 10 minutes. Transfer the lobsters to a platter and tent with foil to keep warm.
Discard all but 2 cups of the lobster cooking liquid. Vigorously boil the remaining liquid in the stockpot, skimming off any foam, until reduced to 1/2 cup, about 9 minutes.
Heat the oil in an 8-inch skillet over medium-low heat. Add the shallot, thyme, garlic, and red pepper flakes and cook, stirring often, until soft, 2 to 3 minutes. Add the tomato paste and cook, stirring, until it darkens slightly, about 1 minute. Add the reduced cooking liquid, increase the heat to medium, and simmer for 2 minutes. Remove from the heat and swirl in the butter, 1 Tbs. at a time, until melted. Season to taste with salt and pepper.
Serve the lobsters with the dipping sauce on the side.