When did Ezekiel the prophet live?

Answer 1

he lived at the time of the First Destruction, some 24 centuries ago.
Ezekiel lived and prophesied before and after the destruction of the First Temple in Jerusalem by the Babylonians, which took place in 586 BCE.

Answer 2

Ezekiel was a priest in the temple at Jerusalem towards the end of the monarchy in Judah, and was then deported to Babylon in 597 BCE, and wrote his book there. The Book of Ezekiel is notable for the careful way in which the author regularly tells us the exact date on which he receives his visions. Either Ezekiel was attempting to assure his sceptical readers that he really did experience these visions before the related prophecies came to pass, or he kept a series of journal notes, dating each one as written, for future reference, but they do provide us some dates to work from. He tells us (40:1) that he received a vision in 573 BCE, so he would have been alive to complete the book some time after that.
The prophet Ezekiel is never mentioned elsewhere in the Old Testament, leading to some debate as to whether his name was a pseudonym, perhaps for a slightly later author, but this view does not have strong support.

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