Soak 8 small wooden skewers in water for at least 15 minutes. In a medium bowl, combine the celery, mint, crushed red pepper, 2 tablespoons of the oil, 1 tablespoon of the lemon juice, and ¹/₄ teaspoon each salt and black pepper.
Heat grill to medium. In a second medium bowl, toss the chicken and onion with the lemon zest, the remaining 2 tablespoons of oil and 1 tablespoon of lemon juice, ½ teaspoon salt, and ¹/₄ teaspoon black pepper.
Thread the chicken and onion onto the skewers and grill, uncovered, turning occasionally, until the chicken is cooked through and the onion is tender, 12 to 16 minutes. Grill the lemon halves until charred, 5 to 10 minutes.
Top the pitas with the celery mixture, chicken, and Feta. Serve with the lemons.
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