The Hoops wrapped up their third consecutive title on Wednesday night and speculation has grown that Lennon could look to leave the club to test himself in England.
But the Parkhead chief executive is eager to hold on to his manager for as long as possible.
Lawwell said: "I think one of the consequences of being successful as a club and as a manager is that people notice and ultimately they might court you. There has been nothing, no approaches for Neil as yet.
"He's a great young manager but Celtic is a big part of Neil Lennon as much as Neil Lennon is a big part of Celtic.
"I am hopeful that Celtic can provide his ambitions and aspirations as a young manager. I haven't spoken with him about it.
"I think if there was something there that was of interest or current then we probably would, but at the moment we are getting on [with things].
"The focus was all about winning the league. Thankfully we've now done that and we start planning for the future and the summer and the Champions League qualifiers."
While Lennon may not head for the exit door just now, the champions are likely to have a fight on their hands to hold on to the likes of Fraser Forster and Virgil van Dijk after impressive seasons.
Lawwell said: "We don't have to sell them.
"Then again, these players hopefully can find what they need and what they want at Celtic. Who knows?
"Maybe we will get some interest over the transfer window but we don't need to sell.
"I hope we can meet the career needs for these guys."