1. In a food processor, pulse the salmon, water chestnuts, panko, and teriyaki sauce until finely chopped. Form the mixture into 3 (1-inch-thick) patties.
2. Place the patties in a single layer in a large nonstick skillet. Cook over medium heat, turning once, until golden brown and cooked through, about 8 minutes.
3. Place each burger on a lettuce leaf, drizzle with teriyaki sauce, top with a tomato slice, and sandwich with another lettuce leaf.