Cut fillet into large chunks. Place fillet, 1 tablespoon tartar sauce, onion, lemon juice, 1/4 teaspoon dill, salt, and pepper in a food processor; pulse 7 times or until blended. Spoon into a bowl; stir in breadcrumbs.
Shape fish mixture into 3 patties; cover and chill at least 1 hour.
Combine remaining tartar sauce, remaining 1/4 teaspoon dill, and cucumber in a bowl; stir well. Cover and chill until ready to serve.
Coat salmon patties with cooking spray. Place a large nonstick skillet over medium-high heat until hot. Add salmon patties, and cook 4 minutes on each side or until lightly browned. Place 1 salmon patty and 1 lettuce leaf on bottom half of each bun; top each with 2 tablespoons tartar sauce mixture and remaining bun halves.