The pair had more than one public bust up in their playing days, and Lennon even threatened to sue the Newcastle legend.
The 42-year-old former club captain stepped down having led the club to three Scottish Premiership titles during his four-year spell in charge.
Lennon has been linked with a number of jobs south of the border but insisted he had nothing in place as he left Glasgow.
Asked for his future plans, Lennon told Sky Sports News: "I've no idea. A holiday, hopefully. I'm away with the club tomorrow for the Champions League final and then I'll take the family away for a bit of R&R (rest and recuperation)."
But the former Leicester City midfielder now looks certain for a return to England after growing frustrated that his attempts turn the club into a European power were hampered by their lack of financial might in the transfer market.
However, controversy has never strayed far from Lennon during his time in Scotland.
He was given a four-match touchline ban following a spat with then Ibrox assistant manager Ally McCoist back in March 2011.
That same month, a parcel bomb addressed to the Celtic boss was intercepted by Royal Mail staff. Two men were later jailed after being found guilty of conspiring to assault Lennon and two other victims.
Lennon was also attacked in the dug-out at Tynecastle in May of that year after a supporter leapt from the Hearts end and charged straight for him.
Despite those ugly incidents, Lennon insisted he had enjoyed his time in Glasgow's east end.
"I have supported Celtic all my life and the club will always be part of me," he said. "It was an absolute honour to play for this great club, to captain the team and of course to become Celtic manager, a position which I cherished dearly. However, I feel the time is now right to move on to a new challenge."
Celtic legend Henrik Larsson has ruled himself out of the running to take charge of the Scottish champions following Neil Lennon's shock exit.
Larsson was immediately made the favourite to take charge at Parkhead after Lennon brought an end to his four-year reign.
However, the retired former Sweden striker has insisted he will not break his contract with Falkenberg.
"The speculation is not correct. I'll not take over as manager of Celtic," Larsson said in the Daily Record.
"I'm flattered to be mentioned and regarded highly. It's natural since I'm now a coach and given my history at Celtic. It's a job with which I'll always be linked.
"I'm at Falkenberg and enjoying it. This is where my focus is. I will not break my contract."
Former Manchester United David Moyes is now joint-second favourite with Sky Bet for the post, along with Malky Mackay.
Owen Coyle, Jackie McNamara, Steve Clarke and Paul Lambert are also in the frame.