Preheat a grill or grill pan to medium high. Toss the onion, banana peppers and 1/3 cup of the pickle juice in a bowl. Whisk the hummus with 3 to 4 tablespoons water in another bowl until smooth and pourable.
Thinly slice the steak against the grain, then cut crosswise into bite-size pieces. Toss with the remaining 3 tablespoons pickle juice, 1 tablespoon olive oil, and salt and pepper to taste.
Brush the pitas on one side with the remaining 1 tablespoon olive oil and season with salt and pepper. Grill, oiled-side down, until lightly toasted, about 1 minute.
Remove the pitas from the grill and top with the steak. Drain the onion and peppers; divide evenly among the pitas. Top with the lettuce and drizzle with the hummus sauce. Top with hot sauce, if desired.
Reheat a grill or grill pan to high. Pulse the olives, shallot, garlic, rosemary, red pepper flakes, 2 tablespoons olive oil and the juice of 1/2 lemon in a food processor; season with salt and pepper.
Pierce the steak all over with a fork and season with salt and pepper. Rub 1 heaping tablespoon olive mixture all over the steak, then set aside, about 10 minutes. Meanwhile, toss the remaining olive mixture with the tomatoes, parsley, the remaining 2 tablespoons olive oil and the juice of the remaining 1/2 lemon in a small bowl.
Grill the steak until browned on one side, about 7 minutes. Flip and cook about 7 more minutes for medium rare. Transfer the steak to a cutting board and let rest 5 minutes. Cut in half; reserve one half for steak sandwiches (at right). Thinly slice the remaining steak against the grain and top with the olive-tomato tapenade.
Recipe courtesy Food Network Magazine