Broad has earned the wrath of Australia's players and fans this summer following a number of incidents during the current Test series, which England lead 3-0 heading into the final match.
The 27-year-old did not walk when he nicked a ball behind in the first Test, while he has also been accused of time-wasting tactics to benefit England when they have been up against it.
The Nottinghamshire man admitted this week that he knew he had hit the ball at Trent Bridge, while speaking of England's win-at-all-costs mentality.
That approach has not impressed Lehmann, though, who has encouraged the Australian fans to make sure that they let Broad know what they think of him when the next series starts on November 21 in Brisbane.
"Certainly our players haven't forgotten, they're calling him everything under the sun as they go past," Lehmann said of Broad's failure to walk in an interview given to Australia radio station Triple M.
"I hope the Australian public are the same because that was just blatant cheating. I don't advocate walking but when you hit it to first slip it's pretty hard.
"From my point of view I just hope the Australian public give it to him right from the word go for the whole summer and I hope he cries and he goes home.
"I just hope everyone gets stuck into him because the way he's carried on and the way he's commented in public about it is ridiculous."
Broad has angered Australian fans further by helping England to their third successive Ashes win, with his brilliant bowling in the last Test securing victory on a dramatic fourth afternoon in Durham.
His popularity with home fans is higher than ever as a result, but Lehmann has no interest in indulging him and went on to accuse him of letting the umpires - much-maligned during the series - take the blame on his behalf.
"He hit it to first slip ... and the biggest problem there is the poor umpire cops all the crap that he gets in (the) paper and Stuart Broad makes them look like fools," he added.
"From my point of view it's poor, so I hope the public actually get stuck into him."
Speaking earlier this week Broad referred back to the Trent Bridge incident, admitting he knew he had nicked Ashton Agar's delivery but Broad claimed his failure to walk was not as clear-cut as it had been portrayed.
''It was an odd one. There was no particular noise because of the noise of Haddin's gloves,'' he said.
''It's a bit silly when people say it was nicked to slip because actually it was edged to the keeper's gloves and flew off the gloves to slip.
''I went down to the other end and Ian Bell was like 'what happened there, I didn't hear anything?' Agar came up to me and asked if I'd nicked it because he wasn't sure.
''So it wasn't as clear cut as everyone had thought, although I knew I'd hit it."