Break cooked salmon into pieces into a mixing bowl. (Make sure the pieces are not too small; when you form the cakes the salmon should look like lump crab does in crab cakes.) Set aside.
In a large nonstick skillet, heat 1 tablespoon oil over medium heat. Add red pepper and green onions; saute until soft. Cool a few minutes, then add to the salmon. Add lemon-pepper, salt, 3 tablespoons mayonnaise, Dijon, egg and 1/2 cup panko bread crumbs. Mix gently. If the mixture seems too loose, add more mayonnaise and more bread crumbs.
Shape the mixture into patties. When all the patties are formed, place the remaining 1/2 cup panko on a plate. Lightly coat both sides of each patty with panko (use more if needed). Set the panko-coated patties on a plate and refrigerate for 30 minutes.
When ready to cook, heat the remaining 2 tablespoons oil over medium heat in the same skillet you used to saute the red pepper and onion. Working in batches if necessary, cook the salmon patties about 3 minutes on each side or until lightly browned. Remove from the skillet; serve on a bed of salad greens. Top with tzatziki, if desired.
To make the sauce, stir together all tzatziki ingredients. Chill for 30 minutes before serving.