In ANSC 117, over the years we have cooked goat carcasses in a cinder-block pit. Obviously, small lamb carcasses would work in the pit, too. For the goats, we have used a large rotisserie to turn the carcass over oak fire and coals to both smoke and cook it for goat tacos.
Here are some photos from different years to show how the cinder-block pit is built. The biggest cinder-block pit is the one we use for cooking pigs. The most recent style uses 16 blocks for a side (total of 32 blocks) and 8 blocks for an end (total of 16 blocks) for a grand total of 48 blocks. We also use these solid blocks on top of the cinder blocks as caps.