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. Return the lobster cooking water 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 halt 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.
Put the egg, tequila, and garlic in a blender, cover, and puree until smooth. Slowly drizzle in 1/2 cup of the olive oil through the feed tube in the top of the blender in a slow but steady stream, until mixture begins to emulsify. Add the lime juice and continue drizzling in the remaining olive oil. Turn the blender off, add the cilantro, salt, and pepper, and pulse to incorporate. Chill if not using immediately.