Combine lemon zest and juice, cumin, oregano, 2 teaspoons garlic, allspice and 1/4 teaspoon each salt and pepper in a 6-quart or larger slow cooker. Add chicken and toss to coat. Cook on Low for 4 hours.
Meanwhile, whisk tahini, water, harissa, the remaining 1 teaspoon garlic and 1/8 teaspoon each salt and pepper in a small bowl. Refrigerate until ready to serve.
Transfer the chicken to a clean cutting board and let rest for 5 minutes. Shred the chicken and toss in a bowl with 1/4 cup of the juices from the slow cooker and the remaining 1/8 teaspoon each salt and pepper. Serve the chicken in pitas with the sauce and lettuce, tomato and onion, if desired.
Equipment: 6-qt. or larger slow cooker