Halve and pit the avocado. Mash 3 tablespoons of the avocado in a large bowl until mostly smooth to form the dressing base.
Add lemon juice, mayonnaise, Dijon mustard, olive oil, garlic powder, and a pinch of salt and pepper to the mashed avocado; whisk until combined.
Dice the remaining avocado flesh and add it to the bowl along with the finely diced cooked chicken, celery, red onion, and chopped parsley or cilantro.
Gently stir to combine, tasting and adjusting seasoning; add 1–4 tablespoons more mayonnaise if a creamier texture is desired.
Serve on toasted bread with extra mayo if desired, or use in a lettuce wrap or with pita chips; best enjoyed immediately.