Fill a large pot with water to come finger deep. Bring to a boil, put the lobsters in head first, and steam 4 minutes. Drain and rinse under cold water until cool enough to work with. Shell the lobsters, wrapping the meat and refrigerating until ready to use (you should have 4 intact claws and 2 tails which you can halve lengthwise). Reserve 12 lobster legs. Reserve the shells, but discard the body. Chop the shells to pieces with a mallet or in the food processor.
Heat 1 1/2 tablespoons butter in a large saute pan and cook the onion until soft. Stir in the tomato paste and add the lobster shells. Pour over the Cognac and flame. When the flames have died down, pour over 3 cups/750 ml water, and cook until the liquid is reduced to 1 1/2 cups/375 ml. Strain, pressing down on the shells to extract all the juices. Return the juices to the saute pan.
While the sauce is reducing, cook the vegetables, separately, in a pot of boiling salted water until al dente, 30 seconds to 2 minutes, depending on the vegetable. When each is done, lift to a strainer with a slotted spoon and immediately plunge into an ice bath to preserve the color.
Bring the lobster stock in the saute pan to a simmer, uncovered. Add the lobster and poach gently 3 minutes. Add the vegetables and continue to cook 2 minutes. Arrange half a tail and a whole claw in each of 4 soup plates. Divide the vegetables evenly around the meat. You should have about 1/4 cup/60 ml sauce per dish, so if you have too much boil it down, whisking in the remaining butter at the end. Taste and season with salt, pepper, and lemon juice. Ladle over the lobster and vegetables, scatter over chervil, and serve.