Place eggs in a saucepan and cover with cold water. Bring to a boil.
Once boiling, turn off the heat, cover the pan, and let eggs sit for 10 minutes.
Drain the eggs and place them in ice water to cool for 5 minutes.
Peel the eggs and chop them roughly.
In a mixing bowl, mash the avocado until smooth.
Add chopped eggs, lemon juice, Greek yogurt (if using), celery, green onion, salt, and pepper. Mix gently until combined.
Toast bread slices if desired.
Spread the avocado egg salad evenly on bread slices.
Top with lettuce, tomato, or cucumber slices if using.
Assemble sandwiches, cut in half, and serve immediately.