Toss the cucumber, bell pepper, onion, parsley, lemon juice, 2 tablespoons of the olive oil, ½ teaspoon salt, and ¼ teaspoon black pepper in a medium bowl. Let sit for about 15 minutes.
Meanwhile, season the fish with 1 teaspoon salt and ½ teaspoon black pepper. Coat with the flour.
Heat the remaining 2 tablespoons of oil in a large nonstick skillet over medium-high heat. Add the fish and cook until opaque throughout, 1 to 2 minutes per side.
Spread the tartar sauce on the buns; sandwich with the fish and lettuce. Serve with the salad and lemon wedges.