The photograph, on a Celtic supporters' group Facebook page, shows an unidentified man holding what appears to be a kitchen knife against a frozen television image of Lennon taken during the midweek Champions League game against Barcelona.
Lennon said the incident was more upsetting for his family than for him, but he raised the matter during his normal weekly press conference yesterday after being asked about the reaction to Scott Brown's red card against the Spanish champions.
When asked if Brown had been hurt by the criticism he had received, Lennon said: "You would do, wouldn't you? You are treated like a criminal sometimes.
"I mean, there's a guy in the paper today holding a knife to a picture of me on a frozen TV screen, but that is sort of laughed off, whereas Scott does something on the pitch and he is treated far more harshly than other people are. You have to have a sense of perspective on this."
Elaborating on the Facebook incident, he went on: "It is not [horrific to see] for me, but it is upsetting for my family. What is concerning is the mindset of some people. Whether it's innocent or they think it's funny, for me it is disturbing. You like to think those days have gone, but obviously not.
"Some people think it's a bit of harmless fun [the Facebook picture]. If it is done in the privacy of the home then fine, but why then put it on a public forum?"
There was less Lennon could say about an incident in which Brown's mother was reportedly punched on the back by a supporter in the VIP section of Parkhead as she defended him moments after he was sent off for fouling and kicking Neymar. "I was only aware of it this morning and Scott didn't mention anything about it to me over the last few days. There is an investigation going on within the club, but I couldn't possibly comment on it."
Meanwhile, Brown will retain his place in Lennon's team when they play host to Motherwell in the SPFL Premiership this afternoon. The captain admitted to making a "mistake" but Lennon was in no mood to punish him.
"He is obviously disappointed, but he has my backing, he has the players' backing and he has the backing of the national team manager [Gordon Strachan] as well. I still feel it was not a red card."
Uefa will decide on October 17 whether there should be any additional punishment for Brown beyond the mandatory one-game Champions League suspension for violent conduct.