The Encyclopedia Americana, 1919

LAMIA, a mythical queen of Libya, who, on being robbed of her own children by Hera, devoted her life to strangling and eating children.

Martin P. Nilsson, Greek Popular Religion, 1940:

These monsters attacked men, sucked their blood, and ate their entrails. Educated people did not trouble about them, but they found a refuge in nursery tales and were cherished by the people. It is characteristic that they became still more popular in the Roman age, during which superstition continually increased. A generic name for such beings was lamia, and whereas the great gods are forgotten, the lamia still lives on among the Greek people. The lamia is mentioned in the Middle Ages, and nowadays it is customary to frighten children with the name. If a child dies suddenly, it is said that the lamia strangled it.

Montague Summers, The Vampire: His Kith and Kin, 1928:

In classical Latin, lamia is defined by Lewis and Short as "a witch who was said to suck children's blood, a sorceress, enchantress." I doubt whether this is a very accurate definition, although possibly it will cover the meaning in Horace, Ars Poetica, 340:

"Ne quodcumque uelit poscat sibi fabula credi,
Neu pransae lamiae puerum uiuum extrahat aluo."

Which Francis translates:

"The probable maintain, Nor force us to believe the monstrous scene, Which shows a child, by a fell witch devour'd, Dragg'd from her entrails, and to life restor'd."

Robert Hunt (editor), Popular Romances of the West of England, 1903:

Another legend relates that it was not the stepmother found by Pengerswick whose "skin was covered with scales like a serpent," but that the lady brought 'home from Palestine by him was an Ophidian--a serpent-worshipper. Hence she became celebrated as a woman possessed by a serpent--having a serpent's power--in fact, a Lamia. This is the only tradition of the kind with which I am acquainted in this county.