Fill a pot with water and eggs and bring to a boil.
Reduce the heat to simmer and cook for 10 minutes.
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 large bowl.
Arrange the whites cut-side up on a serving platter.
In the large bowl mix in the mayonnaise, lemon zest and juice, mustard, salt, pepper and avocado. Process with an immersion blender 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 mixture into the egg whites.