Peel and halve the avocados, discarding pits. Dip all surfaces of the avocados into lime juice to prevent discoloration. Cut two avocado halves into small cubes.
Combine the lime juice with mayonnaise, chives, salt and pepper. Pick over crabmeat to remove pieces of shell, taking care not to break up the crabmeat too much. Add crabmeat and avocado cubes to mayonnaise. Mix gently.
Place lettuce leaves on a serving platter. Arrange the remaining avocado halves on lettuce. Pile crabmeat mixture into the halves. Garnish with capers and olives.