Lake Lucero, New Mexico . . .
During the significant evaporation at the end of the last Ice Age, the grasslands in the White sands National Park region died out. At the same time, ancient Lake Otero receded into the occasional (after rains) Lake Lucero, New Mexico. These are located in the southeast region of the gypsum spread from White Sands National Park. Lake Otero is cited in the various writeups for the now-famous footprints, so I would say that Lake Lucero is the most likely region under archeological investigation.