Cricket Australia had cleared Lehmann of wrongdoing this week following an investigation that saw sacked captain Steve Smith and vice-captain David Warner banned for 12 months.
In an emotional media briefing, Lehmann said his decision was voluntary.
Tearful Smith accepts ‘full responsibility’ in cheating scandal
His resignation came after former test captain Smith broke down in tears of remorse as the three disgraced cricketers at the centre of the Cape Town scandal made apologetic returns to Australia on Thursday.
Smith was unable to complete his news conference at Sydney Airport and was ushered out of the room after a short display of raw emotion during which he repeatedly apologised for his misjudgement.
Batsman Cameron Bancroft spoke of his shame on his arrival in Perth and former vice captain David Warner, scheduled to land in Sydney later in the evening, took to social media to apologise for his role in the cheating.
Cricket Australia bans Smith, Warner for 12 months
Smith and Warner, already stripped of their positions, were handed 12-month bans and Bancroft a nine-month suspension by Cricket Australia on Wednesday for conspiring to scuff up the ball with sandpaper during the third test against South Africa.
"To all of my teammates, to fans of cricket all over the world and to Australians who are angry and disappointed, I'm sorry," Smith told reporters in a prepared statement. "It was a failure of leadership, of my leadership, I'll do anything I can to make up for my mistake and the damage it has caused," he added, breaking down for the first time.
"Cricket is the greatest game in the world. It's been my life and I hope it can be again. I'm sorry and I'm absolutely devastated."
Warner, who was identified as the instigator of the attempt to cheat by the Cricket Australia probe, broke his silence via Instagram, apologising and taking responsibility for his "part" in the scandal.
Ball tampering scandal will haunt Smith forever, says Chappell
"I understand the distress this has caused the sport and its fans," the opening batsman wrote. "It's a stain on the game we all love and I have loved since I was a boy."
Bancroft confessed to having lied about using sticky tape rather than sandpaper to scuff the ball in Cape Town in the news conference immediately after the incident last Saturday.
"I lied. I lied about the sandpaper," the 25-year-old told reporters. "I panicked in that situation and I'm very sorry. I feel like I've let everyone down in Australia."
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