Although "Hot Spot" showed the ball did hit Lyon's bat, "Snicko", a different form of technology, did not detect any contact and Llong upheld the original decision.
"ICC has reviewed the decision and acknowledged that it was incorrect," the ICC said on Twitter.
"ICC confirms the umpire followed the correct protocol, but made an incorrect judgement."
Lyon, on nought at the time, went on to score 34 and help Australia recover from 118 for eight to secure a first-innings lead of 22 which proved crucial in a low-scoring game the hosts won by three wickets.
The decision, made in the first ever day-night test match, was widely criticised by television commentators and New Zealand Cricket contacted the ICC to ask for an explanation.
(Reporting by Ed Osmond in London,; Editing by Neville Dalton)
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