Combine all ingredients for the dip in a small bowl. Refrigerate until needed.
For the lamb, combine first 6 ingredients in a large bowl. Add the lamb and turn to coat. Preheat the barbecue to medium-high. Set the lamb on one side of the barbecue; close the lid. Turn the heat off underneath the lamb; leave the other side set to medium-high. Cook the lamb, turning occasionally, until the desired doneness is achieved – 75 to 80 minutes should cook the lamb to medium to medium-rare.
The best way to gauge doneness is to insert an instant-read meat thermometer into the thickest part of the lamb. For rare lamb, internal temperature should be 130 degrees F; for medium-rare, it should be 135 degrees F; and for medium, it should be 140 degrees F.
Once cooked, allow the lamb to rest for 10 minutes before slicing and serving with the yogurt dip alongside.