I’ve helped with cooking whole (juvenile) goats and pigs, but not a sheep or lamb. We’ve done them on a rotating spit, spatchcocked on a La Caja China cooker, and just whole (wrapped in couple layers of chicken wire so that it was easier to turn them, mostly by hooking that chicken wire with a garden rake). We’ve also halved them to make them easier to handle and speed up cooking a bit. The quickest and most consistent method is with that La Caja China, but those things aren’t cheap. The rotating spit is nice and has a good “wow” factor, especially if motorized. The “chicken wire method” doesn’t look very sexy, but it’ll get the job done.
Timing is the real trick, unless you’re using the La Caja China. As I mentioned, it’s fairly consistent. Since you aren’t worried about flipping the animal, you can easily use a leave-in, probe thermometer to monitor internal temperature. If you follow their directions, you should be done in about 3 hours, give or take depending on all the usual factors.
For the other, open methods, the key is to concentrate your fire on the thicker parts of the animal (shoulders and thighs). You need some fire in the center, but not as much. I can’t give you anything precise, because I have to depend on nothing more than my visual memory, but I want to say you want about twice as much fire (coals, of course) under the thick parts as you do under the thin. Start with a good & hot fire and gradually let the temperature go down–add coals as the cook goes on, but just enough so that the temperature goes down gradually. We placed the grill about a foot above the fire, and we had the spit so that the lowest part (the back) was about 8 or 9 inches from the fire, if I recall. If you have an adjustable spit or grill, you can raise that after the first half hour or hour of cooking to help with cooking temperature. It should take several hours, around 6-7 if I recall.
Seasoning was fairly simple for us–salt, pepper, a little garlic powder. I know the Greek Easter lamb gets more more complex with seasoning, but I’ve never helped with anything like that.
I wish I could be more help, but it’s been a long time since I did anything like what you’re asking, and I never led the cook in the first place. The memories started a little foggy (due to a drink or few), and time hasn’t made them any clearer.
