In a large, heavy pot, bring 2 gallons of water, the bay leaves, onions, 1 teaspoon of salt and peppercorns to a boil. Add the lobsters to the water and simmer, covered, for 10 to 12 minutes. Transfer the lobsters with tongs to a colander and rinse under cold running water. Drain and let cool. When cool enough to handle, break off the claws from the bodies and crack to remove the meat. Twist the tails from the lobsters and discard the bodies. With kitchen shears, cut the underbellies of the lobsters and remove the tail meat. Cut the tail meat into bite sized pieces, and reserve the whole claw meat.
When lobsters are cool enough to handle, break off claws at body of each lobster. Crack claws and remove meat. Reserve some claw meat, covered and chilled, for garnish if desired and cut remainder into bite-size pieces. Twist tails off lobster bodies and discard bodies. With kitchen shears remove thin hard membrane from underside of each tail by cutting just inside outer edge of shell. Remove meat from each tail and cut into bite-size pieces. Spread the claw and tail meat on a plate and place in the refrigerator to cool, about 15 minutes.
In a medium bowl lightly dress the mesclun greens with the olive oil and 1/4 teaspoon salt. Divide the mixture among 4 salad plates. Cut the avocados in half and remove the seeds and skins. Place 1/2 an avocado on each salad plate.
Transfer the lobster meat to a medium bowl. Add the mayonnaise, lemon juice, truffle oil, shallots, chervil, truffle and remaining ¼ teaspoon salt, and toss lightly to just combine. Divide the lobster salad among the 4 avocado halves, and garnish with chives. Serve.