1. To prepare mayonnaise, combine first 5 ingredients in a food processor or blender; process until smooth. Transfer to a bowl; cover and chill.
2. To prepare burgers, place onions, 1/4 cup cilantro, chile, and juice in a food processor; process until finely chopped. Add salt and salmon; pulse 4 times or until salmon is coarsely ground and mixture is well blended.
3. Divide salmon mixture into 4 equal portions; shape each portion into a (1-inch-thick) patty. Cover and chill 30 minutes.
4. Heat a grill pan over medium-high heat. Coat pan with cooking spray. Add patties to pan; cook 6 minutes on each side or until desired degree of doneness.
5. Wipe skillet with paper towels; recoat with cooking spray. Place 2 muffins, cut sides down, in pan; cook 2 minutes or until lightly toasted. Repeat procedure with cooking spray and remaining muffins.
6. Place 1 muffin bottom on each of 4 plates; top each serving with 1 lettuce leaf and 1 patty. Spread about 1 tablespoon mayonnaise mixture over each patty; place 1 muffin top on each serving.