I made this today, and it was declared by one family member to be the best dinner ever! Hint: if one person eats the garlic sauce, everyone must eat the garlic sauce!
Whisk together the lemon juice, vegetable oil, plain yogurt, garlic, tomato paste, salt, oregano, pepper, allspice, cinnamon, and cardamom in a large bowl; add the chicken and toss to coat. Transfer the chicken mixture into a large plastic bag; refrigerate at least 4 hours.
Preheat an outdoor grill for medium-high heat and lightly oil grate. Thread the chicken, onions, and pepper onto metal skewers (or wood skewers that have been soaked in water. Cook on preheated grill until the chicken is golden and no longer pink in the center, about 5 minutes each side.
Mix together mayonnaise, yogurt, garlic, and salt. Cover, and refrigerate.
You can use the pita to make a sandwich with the sauce and grilled ingredients, or just dip everything in the sauce.