Heat the water, thyme, sea salt and lemon juice to a rolling boil in a large saucepot over high heat. Plunge the lobsters, 1 at a time, headfirst into the water. Cook, uncovered, for 12 minutes or until the lobsters float. Remove lobsters and place in an ice water bath until chilled.
For the gochujang-lemon aioli:
Add the egg yolks, garlic and lemon juice to a tall container; slowly add the oil while puréeing with an emulsion blender until emulsified. Add the gochujang paste and blend to incorporate.
For the lobster salad:
To clean lobsters, twist off the arms and remove the rubber bands. Separate each section of the arm with a twisting motion. Poke out the meat in the knuckle section. For the claws, pull back the thumb halfway to loosen, then with a heavy object such as a rolling pin or mallet, strike lightly to allow the full claw to wiggle out when loosened. For the tail, twist off the head section and using a towel, bend the fin area backwards to loosen the tail. This should release the tail meat easily.
Cut lobster meat into large chunks and gently mix with the celery and aioli in a bowl. Fill New England rolls with lettuce and lobster salad; top with tomatoes and green onions.