Make the poaching liquid: Freeze the lobsters for 20 minutes. (This sedates them and makes them more manageable.) Meanwhile, combine 1 gallon water, the bay leaves, thyme, red pepper flakes, paprika, parsley and peppercorns in a large pot. Halve the 4 lemons; squeeze the juice into the pot and then add the halves. Season the liquid with salt until it tastes as salty as the ocean. Bring to a boil; reduce the heat to a simmer.

Kill the lobsters: This is the most humane method: Position the point of a knife on the middle of the back of the head; push the point straight down through the shell and lower the knife through the head. (The lobster may continue to move for a few minutes.)

Poach the tails and claws: Hold each lobster over the pot of simmering liquid and twist the tail away from the body.

Put the tails in the pot and cook 3 minutes, then twist off the large claws (with the knuckles attached), add to the pot and cook 7 more minutes.

Transfer the lobster tails and claws to a bowl with tongs; let cool to room temperature.

Make the aioli: Put the egg yolks, garlic, mustard, vinegar, hot sauce and 1 1/2 teaspoons salt in a food processor; pulse to combine. With the motor running, add the canola oil in a slow, steady stream and process until thick and creamy. Scrape into a bowl and set aside.

Shell the lobsters: Stand each claw on one of its narrow edges and whack the top with a knife. Wiggle the knife until a crack runs through the claw.

Repeat on the opposite edge, if necessary, to make the crack bisect the shell. Pull the claw apart and remove the meat.

Insert the handle of a spoon into each knuckle and twist to pull out the meat.

Lay each tail on its side. Put the palm of your hand on top, then press that hand with the heel of your other hand until the shell cracks.

Hold the tail with the underside facing up. With your thumbs, grab the edges of the bottom of the shell.

Bend back the edges of the shell to crack open the underside and remove the tail meat.

Chop the lobster meat: Pull the flat piece of cartilage from the middle of each piece of claw meat and discard. Halve each tail lengthwise and clean out any visible vein or roe. Cut the claw, knuckle and tail meat into bite-size pieces.

Make the salad: Combine the lobster meat, celery, about 1/4 cup aioli, the tarragon and chives in a bowl; toss. (Cover and refrigerate the rest of the aioli for up to 4 days.) Scoop the lobster salad onto butter lettuce leaves and sprinkle with more chives. Serve at room temperature with the lemon wedges.

Photograph by Jim Franco