The left-arm paceman - a key figure in recent triumphs over England and South Africa - was withdrawn from the ongoing Champions League T20 on Friday due to a rib injury.
However, Johnson is still expected to feature in the first of two Tests with Pakistan, starting on October 22 in Dubai, together with three preceding one-day internationals.
Lehmann told Cricket Australia's official website: "He'll be fine to go. Expect him to play the one-dayers, obviously not the T20 but the one-dayers and the Test series.
"We're lucky enough that in terms of the prep, he did a fair bit of bowling before [getting injured], so it won't be an issue."
A positive update has also been delivered on the progress of Australia captain Michael Clarke, who was forced to make an early return from the recent tri-series with Zimbabwe and South Africa due to a hamstring problem.
"I'm confident [of Clarke featuring in the first Test], he's confident - and that's about where it is at the moment," added Lehmann.
"The tour game [from October 15-18] will be the telling time I suppose, getting him out and playing that ... but I'm pretty confident he'll play."