This very attractive dish with lid seems made for a vanity, where it would presumably have been filled with some sort of cosmetic, or perhaps hair-rings, or perhaps even short swatches of hair or cloth to add to a coiffure.  The piece is, however, utterly without the sort of helpful stain that might identify its original purpose. 

Barely visible on one side are the remains of a handle, though the size of the dish hardly warrents one.  Perhaps this lidded dish imitates in stone something more commonly made of metal or another material. A wooden dish with one handle, of similar size, was found by Petrie at Sedment, in a tomb with other cosmetic containers.