The original Argentinian asado (BBQ) was no more than a humble fire pit. Freshly killed animals (much more fun and tastier if owned by someone not invited) were tied to fallen branches and roasted slowly over the pit.
A few parrilla restaurants in Patagonia still cook lamb, pork and baby goat this traditional way. These days the fire pits are generally in sealed rooms which retain the heat like large ovens. It's worth seeking these places out as the results can be exquisite.
Patagonian lamb pops up occasionally on menus in Buenos Aires. Not surprisingly, it's much more common the further south you head, although I never actually spotted a live lamb roaming the hills of Patagonia.
The slowly roasted Patagonian lamb at La Tablita, El Calafayte, is superb. A crispy exterior gives way to exquisitely tasty and tender flesh - the effect of it being cooked for about four hours at a low temperature and hopefully the lamb's food and life quality.