To make the burgers: place the salmon, onion, scallion, lemon juice, salt and peper in a food processor and process until all the ingredients are blended.
Divide the salmon mixture into 4 patties. Place on a plate and refrigerate for about 20 to 30 minutes.
Meanwhile make the mayo: Place all the ingredients in a food processor or blender and blend until smooth. Transfer to a bowl, cover, and refrigerate until ready to serve.
Heat a pan over medium high heat. Add olive oil and cook the patties for about 7 minutes on each side or to your more or less to your liking.
To serve: Place 1 bun bottom on each plate, top with lettuce, red onion, and 1 patty. Spread the basil mayo on top of the patty and cover with the bun top.