In a food processor pulse the salmon pieces five to ten times until coarsely chopped (but not finely chopped). Transfer the salmon to a large bowl. Add the remaining patty ingredients, including ½ teaspoon salt and ¼ teaspoon pepper, and stir gently to combine. With wet hands, form four patties of equal size, each about 18 millimeters thick. Arrange the patties on a platter, cover with plastic wrap, and refrigerate for 1 hour.
In a medium bowl mix the sauce ingredients, including 60 milliliters oil, and then season with salt and pepper.
Prepare the grill for direct cooking over medium heat (180° to 230°C).
Prepare the grill for cooking over medium heat (200°C).
Brush the cooking grates clean. Lightly brush the patties on both sides with oil. Grill the patties over direct medium heat, with the lid closed, until nicely browned, 6 to 8 minutes, carefully turning once. During the last minute of grilling time, toast the buns, cut side down, over direct heat.
Brush the cooking grates clean. Lightly brush the patties on both sides with oil. Grill the patties over medium heat, with the lid closed, until nicely browned, 6 to 8 minutes, carefully turning once. During the last minute of grilling time, toast the buns, cut side down, over direct heat.
Build each burger on a toasted bun with lettuce, a patty, tomato slices, and sauce. Serve warm.