In a large food processor, combine salmon, bell peppers, celery, onion, garlic, egg, lemon juice, tamari sauce, and dill (if desired). Chop until thoroughly mixed and salmon and vegetables reach a fine consistency, but are not mushy.
Remove from processor and place in a medium bowl. Form mixture into four patties of equal size.
Heat oil in a large skillet over medium-high heat. Place patties in hot skillet and cook for about 5 minutes on each side (turning after 2 minutes per side) or until patties reach desired doneness.
Place 4 lettuce leaves on 4 plates. If using buns place half a bun on each plate.
Remove salmon patties from heat and place on a plate until they cool slightly. After a couple of minutes, place patties on lettuce wraps. (or open-faced gluten-free buns, if desired).
Add Vegenaise® and mustard to one side of each patty and top with tomato slice. Place remaining lettuce leaves on top of burgers and wrap to secure.