Marinate the Lamb:

1. Using a sharp knife, cut several shallow diagonal slashes through the fatty side of the lamb. Season liberally on all sides with salt and pepper.
2. In a large zip-top plastic bag, combine the lemon juice, garlic, paprika, cumin, coriander, ginger, and thyme. Shake to combine, then add the lamb shoulder and seal the bag. Place in the refrigerator to marinate for at least 6 hours, preferably overnight.

Grill the Lamb:

1. Prepare your grill for indirect cooking. If using charcoal, mound the coals on one side and leave a thin single layer of coals on the other. If using gas, turn the burners on one side to high, and the other side to low.
2. Place the lamb fat side down onto the hotter part of the grill and cook over direct heat for 5 minutes or until well browned. Flip over, and grill for 5 minutes longer. (If your lamb is very fatty, you’ll want to have a spray bottle of water handy to control flare-ups.)
3. Once the lamb is seared on both sides, move it to the other side of the grill and finish cooking fat-side down over indirect heat until a meat thermometer inserted into the thickest part of the leg reads 135F, about 15 minutes. Transfer to a platter and tent loosely with aluminum. Let rest for 10-15 minutes, then thinly slice against the grain.

Make the Garlic-Yogurt Sauce:

1. While the lamb is grilling, whisk together the yogurt, garlic, lemon juice, olive oil, and salt in a small mixing bowl. Cover tightly with plastic wrap and chill until ready to use.

Assemble the Wraps:

1. Arrange a few slices of lamb in the center of each pita, then top with cucumber, onion, and chickpeas. Drizzle with yogurt sauce, then fold up to enclose the filling. Serve immediately.