Fill a large saucepan with water and bring to a boil. With a ladle, slowly lower the eggs into the water one by one. Reduce the heat to a low boil and cook for 10 minutes. Drain.
When the eggs are cool enough to handle, remove the shells. Slice each egg in half lengthwise. Remove the yolks and place them in a food processor. Arrange the whites cut-side up on a serving platter.
To the food processor, add the mayonnaise, lemon zest and juice, mustard, salt, pepper and avocado. Process until well blended and smooth, then transfer to a resealable plastic bag. With scissors, snip off a bottom corner from the bag. Using the bag like a pastry bag, pipe the yolk mixture into the egg whites. Garnish with olives. Serve immediately or cover loosely and chill until ready to serve.