JB BANNISTER "a la llama" generally refers to a technique of roasting over flames, not to the animal. Are you sure that isn't what you have run across on the Internet?
Update: There are some traditions that my interest you "Wuatia" from Chile in that its a different cooking technique and using exotic meat, but certainly different from what you are talking about.
Love it...! Why wouldn't you treat the llama as you did the cow? It appears to be an indigenous meat of Peru, and there it's cooked pretty much like beef. BTW: Can I have first dibs on the hide? I could use a new topcoat... Good Luck.
PS: The grilling book, Seven Fires: Grilling the Argentine Way by Francis Mallman may help you.
JB, you are the most ambitious bbq freak I EVER knew of. I have no help at all except to wonder if a Llama would fit in a Caja China, but I suspect you want to be hands-on, or at least mop-brush on with your adventure. The prep. alone is mind-boggling. I've been to a pig roast and the prep. for that was hard enough, and they haven't got that much hair to deal with!!
Anyway, I'm just waiting for your post, "Roasting a whale, need help."