Combine mayonnaise with yogurt and lemon juice in a bowl. Mix in chopped chives.
Combine crabmeat, half or the mayonnaise mixture, chopped cucumbers, chopped tomato and season with salt and pepper.
Place lettuce leaves on each plate and place tomato on the center, opening the wedges so it looks like a flower.
Fill tomatoes with the crab mixture. Serve with the remaining sauce.