Combine 3 tablespoons water, vinegar, and sugar in a medium microwave-safe bowl. Microwave at HIGH 2 minutes or until boiling. Add the celery and let stand for 15 minutes. Drain well.
Meanwhile, combine ¼ cup mashed avocado, mayonnaise, lemon juice, mustard, pepper, and salt in a medium bowl, stirring well until smooth.
Peel the eggs and discard the shells. Slice eggs in half lengthwise and reserve 2 yolks for another use. Chop the remaining eggs and egg whites. Gently stir the eggs, celery, and sunflower seeds into the avocado mixture. Fold in the remaining avocado. Serve with lettuce or bread. Stuff the bread sandwiches with baby arugula or dandelion greens and tomato slices.