The Hoops boss has been linked with a series of top jobs south of the border in recent months and has caught the eye of Premiership clubs for his achievements in both Scotland and the Champions League.
And former Parkhead striker Hartson hopes off-field incidents won't force Lennon to quit the club as he closes in on a third successive top-flight crown.
Hartson said: "He's had threats to his life, he's had bombs through his letterbox, he's been physically beaten up on a public street and abused at games as we saw last weekend.
"I know he's strong-willed and he's a strong character because I sat next to Neil in that Celtic dressing room for five years. But you just wonder. He loves his job, it's a dream job for him having captained the club and played six or seven years there.
"He's at a special place where he would have to seriously consider his options before moving because he loves his job.
"But with all the outside animosity and problems that come up all the time - there seems to be a six-month period where it's quiet and then something else happens again - you would wonder if Neil would have a gut full of it at some stage."
Hartson was speaking at the launch of a golf day in his name that will see a host of famous names from the game, including Lennon and Rangers boss Ally McCoist help raise funds and awareness for testicular cancer charities.
And the Welshman reckons his former team-mate can become one of the all-time greats if he stays in Paradise for the long haul.
He said: "He might well be thinking about titles. Rangers are not going to be challenging for another two or three years so, by then, Celtic could have six titles in a row.
"In fifty years time no-one will question Neil's title wins and say 'ah, but Rangers were out of the league at that point'. No-one will point that out if Celtic win 10-in-a-row.
"Gordon Strachan won three in a row, but the books don't add that Rangers were a poor side under Paul Le Guen.
"Strachan goes down as a three-in-a-row manager. They tell me that when Rangers won nine-in-a-row they were very strong and splashing the cash.
"They had the Gascoignes, Laudrups, Goughs and Souness' of this world. No-one mentions the fact Rangers were in a stronger place as a football club than Celtic.
"Lenny may well be thinking along those lines - he could make himself an absolute living legend along the lines of Jock Stein or Walter Smith."