The Hoops striker is being investigated by his club, the police and the Scottish FA for allegedly singing a song described by the football authorities as being of "an offensive, racist and/or discriminatory nature".
The 23-year-old former Hibernian player was filmed singing with Hibs fans in a pub ahead of their Edinburgh derby against Hearts last month and is alleged to have joined in a chant describing Hearts' former Czech Republic midfielder Rudi Skacel as "a refugee".
The Scottish FA charges, of bringing the game into disrepute and of not acting in the best interests of the game, were added to an earlier charge of singing about Hearts "going bust" and Griffiths is due to appear at Hampden on April 24.
The Celtic manager spoke in October 2012 of a "zero tolerance" approach to racism at the Parkhead club, and he stood by that comment at the club's Lennoxtown training complex on Friday as he addressed the media ahead of the trip to Motherwell in the Scottish Premiership on Saturday.
Lennon, who also said that "any sign of any sort of racism against colour, religion, background will be an instant sackable offence" was also mindful of the fact that Griffiths walked free from court on Thursday after a charge of assault against him was dropped.
Asked if he was confident that the player would still be at Celtic next season, the Northern Irishman said: "Yes."
The Hoops boss added: "There is a police investigation going on and we are doing our own internal investigation as well and they will run parallel with each other and we will take a line from the police on that as well.
"I have spoken to Peter (Lawwell, chief executive) and he has spoken to me about what is going and on and we will deal with it as it comes.
"It will be a joint decision, I would imagine. We will talk it through like we always do with every situation that crops up and we'll deal with it in the way we think is the best for Celtic and what we think is the best going forward.
"There is no question that he has a few issues that we all have in our private life, he has been open and frank about it with me and we will do what we can to help him along.
"He knows now there is a responsibility to the way he behaves, obviously.
"I think at times he does get antagonised by people and at times he has to learn to take a deep breath and walk away and at times that is not the easiest thing to do.
"He has a few adverse headlines over the few weeks but he is our player, my player and if there is a part of re-education or education or educating him the right way then we will do that."
Celtic were convincing 2-0 winners over William Hill Scottish Cup finalists Dundee United at Tannadice in their last outing and Lennon is expecting the same attitude against the Steelmen.
"We will adopt the same attitude," he said. "We want to finish the season strongly. Individual players have targets and we as a team have targets but the be all and end all is to keep this run going.
"We have had one defeat in 33 (league) games so we would like to finish the season with just the one defeat.
"Motherwell are a good side with a good manager and Fir Park is always a good venue."