Rinse the chicken breast and pat dry. Combine 3 tablespoons lemon juice, soy sauce, 1 clove minced garlic and 1 teaspoon of the oregano in a glass dish. Add the chicken, turn to coat, and cover with plastic wrap. Allow the chicken breast to marinate for 30 minutes at room temperature or overnight in the refrigerator.
Combine the tomatoes and feta cheese in a small glass dish. Add the remaining 2 teaspoons lemon juice, 1/4 cup olive oil, and the remaining 1 teaspoon oregano, and stir to combine. Allow to sit at room temperature for 30 minutes.
For the yogurt sauce:
In a small bowl, whisk together the yogurt, 1 clove minced garlic, walnuts, and 2 tablespoons olive oil. Cover and refrigerate until ready to use.
Preheat a grill to medium heat.
Spray a grill basket with olive oil. Grill the chicken breasts over medium heat for 8 to 10 minutes, until no longer pink in the thickest portion of each breast. Spread the onion rings over the surface of the basket and grill while the chicken is cooking. Turn the basket frequently. The onion rings will blacken as they cook; this will also take 8 to 10 minutes. When the chicken and onion rings are cooked, place the pita breads on the grill for about 2 minutes per side, until grill marks show. Slice the chicken into very thin pieces.
At serving time, put out all of the ingredients and allow each person to assemble sandwiches: Split each pita. Place several slices of grilled chicken, 3 or 4 slivers of onion, a tablespoon of tomato-feta mixture, lettuce, olives, and 1 or 2 slices of bacon into each pita. Top with yogurt sauce and a wad of alfalfa sprouts. Add salt and pepper, to taste. Fold up the sides of the pita and enjoy!