Lehmann, 54, played 27 Tests for Australia. He was Australia coach for four of the Ashes series Root has played in.
Root was emerging through the ranks when Lehmann was at Yorkshire, with whom he was overseas player until 2006.
Lehmann will join county side Northamptonshire as head coach for the 2025 season.
“I’ve not spoken to him for a while,” added Root.
“I’ll do my job and he can do his job. He’s completely entitled to say what he wants. That’s his right.”
After his initial comments, Lehmann later wrote on X: “Just to be clear as there are a lot of people who think that I think Joe Root is not a great.
“He is going to be a great, I know that and a wonderful ambassador for our game, but needs and he will probably do this next Ashes. Get a hundred in Australia and then no dispute.”
Root passed Sir Alastair Cook in the first Test in Pakistan in October to become England’s all-time leading runscorer. With a tally of 12,754, he sits fifth on the all-time list, behind Sachin Tendulkar, Ricky Ponting, Jacques Kallis and Rahul Dravid.
Regularly bracketed alongside Kohli, New Zealand’s Kane Williamson and Steve Smith of Australia in the ‘Fab Four’ of Test batting, Root has enjoyed the best form of his career since the beginning of 2022.
In that time, his 3,223 runs are comfortably more than any other player in Test cricket and includes 12 hundreds.
In Christchurch he will become only the fourth Englishman to reach 150 Test caps, after his former team-mates Cook, James Anderson and Stuart Broad.
“It’s a lot of fielding, isn’t it?” he said. “It’s really nice to have played as many games as that and still be going.
“In many ways it feels like just another game. I’ve got a lot more to offer this team and this shirt.
“It will be nice to try to start the series well and get us off to a good start.”
The first match of the three-Test series starts at the Hagley Oval on Thursday (22:00 GMT, Wednesday).
