The Hibs head coach has offered to speak to Griffiths to help him through the off-field issues which have prompted Celtic to take him out of football and seek professional help for him.
Lennon - who signed Griffiths for Celtic in January 2014 - has previously spoken openly about his own battle with mental health problems, which affected him from his playing days onwards.
“Sometimes it builds and builds and builds in an individual and then they sort of tip over the edge. They just need support,” said Lennon, whose team host Celtic on Sunday.
“He’s a human being, we all have issues, and unfortunately for Leigh, his are played out in the public eye.
“We all want him to make a speedy recovery. I don’t know what the issue is or the problems he’s having, but he’ll come through it with support. And he needs to talk about it and deal with it as quickly as possibly.
“It’s part of the recovery, talking about it, getting professional help and looking after your well-being physically. Because it does affect you physically as well as mentally.
“From everyone here at Hibs, we wish him a speedy recovery, and anyone else who is going through it in the football world. It’s such a common illness now, that affects so many people in so many different ways.
“What you do is you lose control. You lose control of your emotions and you lose control of your mind to a certain point.
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“Not being psychotic or anything like that, but the mind plays tricks on you and makes you think very, very differently from what you would when you are feeling normal.”
The 47-year-old added: “No question, he will get better. It’s obviously been an accumulation of things which has built up and built up.
“In a few weeks time he will be on the mend, there’s no question of that, if he does the right things. “But it’s a difficult period for him. He may need a bit of privacy but he will need a lot of support as well, particularly from his family.”
When asked if he would be willing to speak to his former player, Lennon said: “No problem - I have done that with many players and many people in different walks of life as well. “I have been very public with it over the years and I have no problem with that at all, I think it’s important.
“It has probably been there from the year dot but maybe people in the 70s, 80s and 90s weren’t keen to talk about it or didn’t know what was happening to them. “Now we are more aware of it, it can be remedied quicker rather than suffering in silence.
“Because sometimes you can feel a little bit desperate. It may be his first episode if it, hopefully his last, and maybe he didn’t know what’s going on in his own body and his mind. And that can be a scary prospect sometimes.
“Now that it’s out in the open and Celtic are doing all they can to help him - there was a great banner at the game last night in support of him - he just needs time.
“We may not see him between now and the end of December but hopefully by the time the season restarts again, he will be back to his normal self.”