Lennon was asked about the managerial vacancy at Sunderland on Monday, but insisted he had not considered a move to Wearside as a possibility.
Since taking over the reins at Parkhead in 2010, Lennon has guided the Hoops to two Scottish league titles, two Scottish Cup triumphs and the last 16 of the Champions League.
With Celtic back among Europe's elite again this season, the 42-year-old Northern Irishman's stock continues to rise.
However, Lawwell believes Lennon is committed to the Celtic cause and would only leave Glasgow for a truly unmissable opportunity.
"It would take something special to lure him away," Lawwell told the Daily Record.
"This is a special club. It's a special job. If I was advising him as a friend, it'd have to be something different.
"If he continues to do as he is, then there will be approaches. It's inevitable.
"But he's focused on what we're trying to do and he buys into it. He's given me no indication that he wants to do anything else. He's a Celtic guy and that is a big plus."
When asked if he was a contender for the Sunderland job ahead of the Hoops' Scottish League Cup home tie against Morton on Tuesday night, Lennon distanced himself from speculation.
"I'm not aware of me being linked with anything. You are asking the wrong person," he told Sky Sports News.
"I don't like answering questions on this kind of thing.
"Maybe you should ask the people linking me with the jobs. I'm not aware of who they are. I'm very happy doing what I'm doing at the minute."