A sphinx.

The Enc. Britt. has some interesting observations: Through Egyptian influence the sphinx became known in Asia, but its meaning there is uncertain. The sphinx did not occur in Mesopotamia until about 1500 BC, when it was clearly imported from the Levant. In appearance the Asian sphinx differed from its Egyptian model most noticeably in the addition of wings to the leonine body, a feature that continued through its subsequent history in Asia and the Greek world.

On the Karatepe site some have (and they probably all had at one time) eyes that are made more impressive by adding a lead pupil.