Chop 1 pound of the salmon into small, ¼ inch cubes and place into a large bowl. Place the remaining salmon into a food processor, and blend with the lemon zest and juice, mayonnaise, black pepper, Dijon mustard, dill, red pepper flakes, and salt. Pulse until a mostly smooth mixture is formed.
Fold the green onions, panko breadcrumbs, and pureed salmon into the salmon pieces until combined. With your hands, form the salmon burger mixture into 5 patties, ¾ inch thick, depending on the size of your buns/rolls.
Place the burgers on a sheet pan or plate that has been lined with parchment paper and brushed with olive oil. Make sure both sides of the burgers have been lightly brushed with oil to avoid sticking on the grill. Cover the burgers and refrigerate while the toppings are prepared.
For the remoulade, simply whisk together the mayonnaise, lemon zest and juice, dill, Dijon mustard, garlic powder, and capers. Season with freshly ground black pepper and salt to taste.
Carefully wash and dry the butter lettuce leaves and slice the avocado.Split the buns/rolls and brush the cut-sides with olive oil. Heat the grill on medium-high to high heat. Carefully place each burger on the grill, cover, and cook for 4 minutes, until grill marks are formed. Gently flip the burgers, being careful not to tear them during flipping. Cook another 3-4 minutes until the burgers spring back slightly when pressed in the center or are 150-160 °F inside.
Cover the burgers and toast the buns, cut-side down, on the grill, for 2 minutes or until slightly crisped.
Serve the burgers on the buns, topped with the remoulade, a few leaves of lettuce, and a few avocado slices.