Remove the lamb from the cooler and allow it to rest for about an hour.
Light the charcoal in the chimney.
Lamb Seasoning
Combine the kosher salt, black pepper, garlic powder, onion powder, dried oregano, and dried thyme in a small bowl.
Lamb Preparation
Spread olive oil over the lamb and rub it in, making sure to coat the whole thing.
Squeeze half of a lemon, getting both top, bottom, and sides.
Sprinkle the lamb seasoning over the entire lamb. Optional: Butcher tie the lamb before cooking to help hold its shape.
To Cook
Pour the charcoal into the grill, then place the grill grate and lid on, making sure to open the vents fully. Allow the grill to heat for 10 minutes. Optional: Place a tin foil pan into the charcoal to catch the lamb drippings while cooking.
Place the lamb in the center of the preheated grill then give a slight drizzle of the lemon. Cook for 1 hour and 10 minutes.
While waiting, prepare the garlic sauce and the wrap components.
After 35 minutes add another fresh squeeze of lemon to the lamb.Tip: Remove and replace the lid as quickly as possible to prevent heat loss.
Check the temperature to make sure the lamb has reached 165 degrees F. Remove the lamb from the grill and let it rest under some tin foil for 30 minutes.
Garlic Sauce
In a mixing bowl, add the plain yogurt, lemon juice, chopped garlic, a pinch of salt and pepper to taste, then stir together.
Vegetables
Prepare the vegetable by slicing the red onions, dicing the tomato, and thinly slicing the lettuce into strips.
To Serve
Cut the lamb into cubes or thin strips.
Lay out the 6 pita breads flat on their own piece of foil.
On the 6 pita bread, divide the garlic sauce, lamb, tomato, and lettuce equally, and then top with the onion.
Roll each pita bread to create a wrap, then roll each created kabab in the foil to hold it together.