I think that I have seen all 4 of the lions, as they were youngsters at the Oklahoma City Zoo when I visited in the summer of 2008. In regards to this photo, what is on top of the large brick structure? That thing looks like part of a castle!
Those are wood logs sticking out of the roof. My best guess is that it is an attempt to blend exotic "ancient temple" architecture with local native american architecture. That type of architecture from the Pueblo Indians, with roof beams sticking out the side of a square adobe building, is commonly used throughout New Mexico. Even though El Paso is just across the border in Texas, it is much more a part of the southern New Mexico region.