Put 1 gallon of water in a 6-quart stockpot over high heat. Add the onions, carrots, celery, garlic, bay leaves, vinegar, lemon juice, lemon rinds, salt, and cayenne pepper. Bring the pot to a boil and cook for 15 to 20 minutes. Add the lobster and cook until red and cooked through, 7 to 8 minutes. Transfer to a bowl filled with ice water to halt the cooking. Once the lobster has cooled, remove from the ice bath and set aside.

Bring the poaching liquid back  to a boil. Add the shrimp to the pot. Cook until the shrimp are just cooked through, 2 to 3 minutes. Transfer to a bowl filled with ice water to stop the cooking. When the shrimp have cooled, remove from the ice bath and set aside.

Crack the shell of the lobster and remove the tail and claw meat. Chop the meat into 1/2-inch pieces and set aside.

To serve, place a quarter of the greens into the bottom of each of 4 large, chilled martini glasses. Drizzle a little of the mayonnaise over the greens. Divide the tomatoes, avocado, shrimp, and lobster meat among the glasses. Drizzle more of the mayonnaise over the cocktail and garnish with fresh cilantro. Serve immediately.