Lower Egypt was the area of the Nile delta in ancient Egyptian history. It was north of Upper Egypt.
The earliest Egyptian sites are in Lower Egypt and the Faiyum depression, where Neolithic remains date back to 5300 B.C. Upper Egypt's neolithic settlements date only from about 4500 B.C.
Source: Neil Asher Silberman, Diane Holmes, Ogden Goelet, Donald B. Spanel, Edward Bleiberg "Egypt" The Oxford Companion to Archaeology. Brian M. Fagan, ed., Oxford University Press 1996.