1. Break off claws from each lobster at the knuckle. Separate tails from bodies by twisting. (Reserve lobster bodies for another use.) Discard the heads. Using scissors, cut along the underside of the shell of each lobster. Remove the shell, keeping the tail meat in one piece. With a knife, devein each tail. Break off the small section of each claw. Using the back of a heavy knife, crack the large section of each claw. Remove the shell, keeping the claw meat in one section. Cut knuckles apart with scissors and remove meat. Cut meat into cubes, reserving claws for garnish.

2. In a large bowl, combine cubed lobster, peppers, avocado, cucumber, tomatoes, onion, olives, salt, and pepper. Add all but 2 tablespoons of the dressing; gently toss. Add the croutons, and let the mixture stand for 10 to 15 minutes, then toss again. Line a large platter with greens, and drizzle with the remaining dressing. Transfer salad to platter. Garnish with reserved lobster claws and basil leaves.