Rinse the chicken breasts and pat dry.
Combine 9 teaspoons lemon juice, soy sauce, garlic and 1 teaspoon oregano in a zipper bag. Add the chicken, seal, turn to coat. Allow the chicken breasts to marinate for 30 minutes at room temperature or overnight in the refrigerator.
In a small bowl, combine tomatoes and feta cheese. Add remaining 2 teaspoons lemon juice, olive oil, and remaining 1 teaspoon oregano; stir to combine. Allow to sit at room temperature for 30 minutes.
For the yogurt sauce, in a small bowl, whisk together the yogurt, garlic, walnuts and olive oil. Cover and refrigerate until ready to use.
Preheat a grill to medium heat.
Grill the chicken breasts over medium heat for 8-10 minutes, until no longer pink in the thickest portion of each breast.
Spread the onion rings on the grill while the chicken is cooking, turning frequently. The onion rings will blacken as they cook; this will also take 8-10 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, yogurt sauce, 3 or 4 slices of onion, 1 tablespoon of tomato-feta mixture, lettuce, olives, and 1 or 2 slices of bacon into each pita.