Preheat the grill to medium-high heat.
In a food processor, add the salmon fillets and pulse until finely chopped but not pureed.
In a large bowl, combine the chopped salmon, breadcrumbs, mayonnaise, Dijon mustard, lemon juice, garlic powder, onion powder, salt, black pepper, and parsley. Mix until well combined.
Form the mixture into four equal patties, about 1 inch thick.
Lightly oil the grill grates to prevent sticking. Grill the patties for about 4-5 minutes on each side, or until cooked through and slightly charred.
While the burgers are grilling, prepare the avocado salsa by combining the diced avocado, tomato, red onion, and lime juice in a bowl. Gently mix to combine and season with salt to taste.
Toast the hamburger buns on the grill for 1-2 minutes until golden brown.
Assemble the burgers by placing a salmon patty on each bun, topping with lettuce and a generous scoop of avocado salsa. Serve immediately.