The left-handed Warner only averages just more than 30 after 25 innings on Asian surfaces compared to scoring an average of 60 runs per innings on home soil.
Warner has also only struck one century in Asia while his highest score was 56 in Australia’s four-match Test series in India earlier this year, which the Aussies went on to lose 2-1.
However, Lehmann feels the 30-year-old has matured over the years and can now adapt his game to the surfaces on the subcontinent.
Australia play the first of the of their two Tests against the Tigers from 27-31 August in Mirpur with the second game schedule for 4-8 September in Chittagong.
Speaking to Cricket Australia’s website, Lehmann said of Warner: “I think he’s realised what he can and can’t do.
“I’m pretty confident that he’s going to turn his form around on the subcontinent.
“He looks good from what I’ve seen of him so far, and he got starts in India (earlier this year) without going on.
“If he goes on, then we’ll have a really good series in Bangladesh. So for him, and for the team, we need him to make big runs as he normally does (in Australia).”