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Flower departs after two years in charge during which Lucknow made the playoffs and finished third on both occasions.
McDonald and Vettori have a working relationship from the Indian Premier League, where they played and coached together at Royal Challengers Bangalore.
On Wednesday, Cummins spoke for the first time since Langer's resignation, saying the team needed a 'new coaching style' for the future.
Langer resigned on Saturday, just weeks after leading Australia to a 4-0 Ashes series win over England, with CA saying he had rejected a short-term extension of his contract.
Langer was reported to have reacted angrily during a recent meeting with CA over his contract and had been asked to reapply for the role.
A source-based report in the Sydney Morning Herald said, the 50-year-old was given a "strong and straightforward" feedback about his coaching style.
Australia lost the series against India 2-1 but would have qualified for the final in England ahead of New Zealand had they not been penalised for slow over rates.
Sydney Morning Herald quoted sources as saying that Langer's approach and difficulty coping with pressure was "increasingly incompatible with a team consisting largely of experienced players in their late 20s or 30s".
The Australian head coach questioned the timing of last year's IPL.
Warner is expected to replace the dropped Joe Burns but selectors will have to decide whether Pucovski should partner Warner at the top of the order or retain Matthew Wade as a makeshift opener.
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