Ancient Inventions by Peter James and Nick Thorpe lists several types of lock. The "Homeric lock" is mentioned in the Odyssey. Penelope uses "a cleverly made copper key with an ivory handle":
She quickly undid the strap attached to the door handle, thrust the key through the hole, and with a well aimed thrust shot back the bolt. The key did its work. With a groan like a bull roaring in the meadow, the doors flew open before her".
A bolt was pulled in to position using a cord which passes through the door to the outside. To unlock the door, an L shaped rod is passed through another hole, and pushes against a protuberance on the bolt.
The "Egyptian lock" was invented Assyria, and the earliest known example was found in Khorsabad, in the palace of Sargon II (721-705BC). This is really interesting, because it is a tumbler lock, conceptually similar to the modern cylinder ("Yale") locks. Rather than a cylinder, there was a box with several pins above the bolt. When the bolt was closed, the pins would fall down to rest in holes in the upper surface of the bolt, preventing it from being opened. The pins could be pushed up and clear by using a key with several fixed pins, which could be used to push the moving pins up out of the holes, allowing the bolt to move.
The earliest key is a really odd device and difficult to describe, so I've put up a scan here. The keys were first found as grave goods for women in Egypt in 1887, and then bronze versios were found in women's graves in Sicily. Their purpose was only discovered in 1907 when it was noticed that they were still in use in Ethiopia.