Police are investigating the latest attack on Lennon after missiles flew past his head as he watched the League Cup semi-final between Aberdeen and St Johnstone at Tynecastle last Saturday.
During his time in Glasgow, Lennon has suffered attacks in his car, death threats daubed on the road outside his home, been knocked out in a street attack, had bullets sent to him in the post, been attacked by a Hearts fan during a game, and was a victim of a letter-bomb campaign that saw two men jailed for five years.
"I don't want it," the former Northern Ireland international said.
"I don't need it. I'm not happy with some of the stuff that has come out regarding myself in terms of journalists saying, 'He attracts it, it's his controversial, confrontational nature'.
"For me, that's very irresponsible. I am no more confrontational than any other manager in the SPFL. However, when it's an issue regarding me, it seems to be imbalanced.
"You cannot have people throw coins at you when you are sitting there trying to do your job. And yet some people in the back of their minds think it's my fault. Why this happens, I don't know.
"In the past there is no question there were sectarian elements to what happened to me. People want to bury their head about that. I don't, I want it said and I want something done about it. Last week there was no evidence of a sectarian element, but certainly a hooligan element."
Lennon added: "It's getting harder to comprehend because I don't think I have done anything to warrant it. I think my players, myself, my backroom team conduct ourselves in the best way.
"When there are flashpoints, which happens to every manager, it gets highlighted and blown into the stratosphere.
"I see managers every week losing the rag. I don't complain because I understand how they feel. But there's no pictures of them the next day going up to the fourth official and being abusive or squaring up to another manager. But when I'm involved it's front and back page."
The former Celtic skipper is frustrated at public perceptions of him.
"I look at some of the comments - 'He was a thug on the pitch'. No I wasn't. I never lifted my hand to anyone, never two-footed anyone, never elbowed anyone. I played the game aggressively, which was my job.
"'He brings it on himself.' In what way? Do I go down the street looking for it? Anyone who knows me away from football knows the type of person that I am. Anyone who knows me within the game knows that I want to win, and I'll do anything I can within my power to do that. People don't like it and people use other excuses to vent their fury on me."
Lennon, speaking during his media conference ahead of the William Hill Scottish Cup clash with Aberdeen, called on others to help change his public persona.
"I have certainly tried to do that and it's not working," the 42-year-old said.
"I don't think the condemnation is enough. Sometimes I get the feeling that, 'It's Lenny, he can take it, he's a stand-up guy, he's a street-fighting man'. All that c**p. I'm fed up with it.
"I don't go street-fighting. I look after myself and my friends and family. I live my life as quietly as I can away from football but I'm in the public eye.
"But a lot of the stuff has been almost life-threatening and the condemnation has been nowhere enough."
When asked whether he was close to the tipping point and might quit Celtic, Lennon said: "I don't know, I don't know. It's a lot to give up and I don't really want to do that if I can avoid it."
After a pause, Lennon added: "No, it hasn't come to that point yet, certainly not. What will determine it is if things go wrong on the pitch. And that will be determine by other people, not me.
"It may be my decision further down the line, but I'm not picturing that scenario. I want to be as successful as I can for as long as I can.
"I love being the manager of Celtic. It's a privilege, an absolute honour. And I don't want to give it up because I worked very, very hard to be in the position I'm in.
"That's the reason why I haven't walked. It's a prestigious job, a precarious job if you look at what's going on in England, a lot of sackings.
"Being the manager of Celtic, there are only 17 other people who have done it, and that means a lot to me."
Lennon hopes the Tynecastle incident does not lead to any hostility when Derek McInnes brings his team to Parkhead.
"I don't think it's fair on Aberdeen," he said. "I have a great relationship with Aberdeen, we do as a club. I get on very well with Derek, I have tremendous respect for him. This isn't going to sour those relationships.
"However, I want the perpetrators accounted for."
Meanwhile, Leigh Griffiths is bidding to make his Celtic debut against Aberdeen in the William Hill Scottish Cup fifth round.
Celtic manager Neil Lennon revealed full-back Adam Matthews (calf) was "touch and go" while James Forrest is a "major doubt".
Long-term absentees Mikael Lustig (hip), Beram Kayal (foot) and Steven Mouyokolo (Achilles) remain out.
Provisional squad: Forster, Fisher, Ambrose, Van Dijk, Izaguirre, Brown, Mulgrew, Boerrigter, Forrest, Griffiths, Commons, Pukki, Balde, Biton, Samaras, Stokes, Johansen, Matthews, Henderson, O'Connell, Zaluska.