The 23-year old remains under investigation for alleged racist chants directed at Heart of Midlothian great Rudi Skacel, which occurred alongside Hibernian supporters, who also sung in a derogatory manner towards their Edinburgh rivals regarding their financial trouble.
Griffiths scored a goal and had a hand in two others as Celtic hammered Inverness 6-0 at Parkhead on the weekend but was the target of derision from some sections of the Hoops crowd who displayed banners criticizing the former Wolves forward.
The banners read: ‘A man must be a Celt on and off the field otherwise he is of no value to this club' and 'refugees welcome, created by immigrants'.
After the match, Lennon admitted he wasn’t exactly sure who the banners were for but was quick to leap to the defence of Griffiths who has now netted seven times in 11 Scottish Premiership appearances since arriving in January.
"I can't comment on the banner because I wasn't sure who it was aimed at for a start," Lennon said.
"If it was aimed at Leigh then we are going through a process at the minute and we will be able to speak more about it when the process finishes.
"We've all made mistakes. But I think the kid will come good. I think he'll learn from it and have a good career here.
"I don't know if he was aware that the banner was aimed at him. If he did then we expect those kind of performances from him anyway.
"I think that's seven goals in 11 games so he's doing exactly what we brought him in to do."
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