I've smoked lamb chops a few times - they were a real treat - last time marinated in a chipotle, lime, cilantro mixture!
Smoked stuffed lamb breast that was ok - only because the stuffing was not real good
Smoked lamb ribs - man are they fat, but pretty darn good eats - hit them with a rub (don't remember which) and lots of pepper and some salt - for some reason the ladies liked them.
And I like to smoke leg, but I like to debone and butterfly - lamb spatchcock? That way it doesn't take as long and more surface to absorb smoke flavor. Usually go simple on the rub - just slather with oil (walnut oil is good) and sprinkle with garlic (fresh or granulated), salt and pepper. Timing and when to pull change almost everytime I do it. It is usually tender enough, so don't have to go too low or too slow. Butterflied like this it can be smokey grillied almost, especially since I like it rare!
I think I've used hickory, hackberry, oak, and mesquite on it at different times. I recently bought some Cherry pucks just for an idea I had for doing my next lamb leg.
Never smoked a whole lamb shoulder - never have I noticed one for sale. Must be good eats and you Brits and New Zealanders must keep them to yourselves.

(sorta like the Cali's do with tri-tip) My Dad's family is from the Hill Country of Texas and own some pretty good sized ranches (20,000 acres) and years ago when we had a reunion - man, there was some barbecue cooked. It would take two or three days to cook as there was half calves, whole hogs, and whole goat, whole deer, whole wild turkey, whole javelina, fresh sausages, etc.... but my favorite was the whole lamb. Only time I had access to eat it and I took advantage of the opportunity. Definitely low and slow over Oak - probably a mixture of Live Oak and Post Oak with some Mesquite thrown in for good measure - and if my memory serves, there was no fancy rub, just salt and pepper - and a whole lot of a mustard, beer, lemon, butter, onion mop! To give you some idea of how much meat this was and how big of a pit, the mopping sauce was kept in a wash tub and a normal mop like you would use on the floor was used to to mop everything. The lambs, as well as the rest of the carcasses were laid out flat over the pit. Man that was tasty.