Pulse avocado, mayonnaise, lime zest and juice, and evoo in a food processor or blender until it becomes a creamy and a thick puree. Make ahead tip: place in a jar or covered container and store in the refrigerator for up to 2 days.
Toss hearts of palm, celery, and scallions together in a bowl and season with salt and pepper.
Divide hearts of palm mixture between lettuce cups and drizzle with avocado dressing. Garnish with pomegranate seeds and chopped flat-leaf parsley as desired.
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