Speaking after a week in which his Scotland international, Charlie Mulgrew, tweeted a mock naked picture of his lookalike hugging a naked model, the manager revealed that he has spoken to his players about the requirement for common sense.
Lennon himself is no stranger to the medium, and has been involved in a few stand-offs with punters over the last 18 months or so.
As such, he has some sympathy for the ease with which players can be sucked into ill-advised public slanging matches, but he has insisted that the message of sensible usage has to hit home.
"It is not just the players but the players' wives as well," he said. "I have told the players that anyone damaging the reputation of the club will be heavily fined and we may have to stop them using it altogether.
"There have been episodes that I have taken a pretty dim view of. We have made it pretty clear that there is a certain line that you can't cross. Charlie putting up naked pictures perhaps wasn't one of his brightest ideas and he will be punished for that.
"I don't mind Twitter. Everyone looks to the bad things, but there are good things about it too. I did that 10k run last week and I raised a lot of money and if I hadn't had Twitter I probably wouldn't have raised anywhere near that. So there are benefits but like everything else there are drawbacks too.
"I do have some sympathy but they should be experienced enough now to know what they can and can't do on a public site."
Lennon himself was involved in a Twitter dispute this week with Rowan Vine after the Hibs striker threatened to get his "mate" Alan Shearer to kick Lennon in the head again.
And while the Celtic boss accepted Vine's climbdown and subsequent apology he will expect the authorities to deal with the comments.
"It is something that I am assuming the authorities will look at, rather than myself," said Lennon. "There's nothing I can do about it. I don't run the game. I don't make the laws up. I think there's a line you can't cross when it comes to saying anything in public, either personal or against a club."
Meanwhile, Celtic will also hope that Scott Brown's presence in person at his Uefa appeal next week will encourage the disciplinary committee to go easy on the midfielder.
The Celtic captain was handed a three-game suspension by Uefa for his petulant kick at Neymar in the defeat to Barcelona at the beginning of October. Celtic are hoping to have that punishment eased at an appeal which is expected to take place on Tuesday.
"The club lawyer and secretary will be there, but I think it is important that Scott goes," said Lennon. "I think it is better if he puts his case across.
"Other people have gone. John Terry went to his and got it reduced so we are hoping that there will be some semblance of fairness and I am sure there will be."