Chop the salmon fillets into small pieces and mix in a bowl with breadcrumbs, egg, lemon juice, salt, and pepper until well combined.
Form the mixture into patties about one inch thick and set aside.
Preheat your grill to medium-high heat (375°F).
Grill the patties for 5 minutes on each side until cooked through and grill marks appear.
While grilling, combine diced avocado, tomato, cilantro, and lime juice in a separate bowl to create the salsa.
Once the salmon patties are ready, assemble them on toasted buns topped with avocado salsa.