Combine all of the marinade ingredients in a resealable plastic bag. Add the salmon, seal the bag and refrigerate for at least 30 minutes, or up to 1 hour.
Combine all of the tomatoes and onions ingredients in a large bowl and set aside until ready to assemble the gyros.
Combine all of the ingredients for the dill cucumber sauce in a small bowl. Cover and refrigerate until ready to serve, at least 30 minutes, or up to 12 hours.
Preheat the grill if using outdoors, or preheat indoor stovetop grill pan over medium-low heat.
Remove salmon from the marinade and grill until cooked through, about 3 to 4 minutes per side. Remove from the grill to a plate and keep warm.
Put the pita bread on grill to heat through.
Serve by cutting pitas in half, filling them with salmon, and topping them with the tomato mixture and the cucumber dill sauce. Add iceberg lettuce, if desired, and serve.
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