(This piece is actually from the Brooklyn Museum, but she's the same type as the ones at the Met:
 

 
Bust from an Enthroned Statue of Sakhmet
Granodiorite, New Kingdom XVIII, reign of Amunhotep III (circa 1390-1352 B.C), from Thebes
Brooklyn Museum 1991.311
(from the info card)
"The goddess Sakhmet, whose name means 'The Powerful One,' was worshipped at least as early as the Old Kingdom. In the New Kingdom she became the wife of Ptah, chief god of the Lower Egyptian capital of Memphis. She also became closely associated with Mut, wife of Amun, king of the gods at the Upper Egyptian capital of Thebes. Together these goddesses could represent the unity of Upper and Lower Egypt, conceived of as a duality."

 

Sekhmet, Egyptian Goddess of wrathful protection


Notice the rosetta pattern over each nipple, an ancient leonine motif that can be traced to observation of the shoulder-knot hairs on lions.

 

 

"It is thought that the black granite statues of Sekhmet, now scattered in museums throughout the world, once formed a huge monumental litany in stone. Jean Yoyotte has estimated that over seven hundred of them must have once stood in the now ruined funerary temple of Amenhotep III, on the west bank at Thebes, each dedicated to a particular day of the year. Alternately seated and standing, each lioness figure is crowned with a solar disk and fiery cobra snake, and holds either an Ankh-sign of life, or a papyrus sceptre, to symbolize the life-giving greenness of her propitiated state." Hathor Rising, by Alison Roberts, page 13