The midfield dynamo is under contract until next year, with the club holding a further 12-month option on the deal signed in 2011.
Now injury-free, Brown is confident his career has many years still to run and has revealed he wants to "stay here as long as possible."
That's music to the ears of Lennon, who is delighted with the form his skipper is showing as he leads the club to a third consecutive league championship.
Ironically, Lennon reckons it is only Brown's consistency - without any significant peaks or troughs in performance - which allows people to overlook his contribution.
"I think that's right - I was like that," said Lennon with a rueful smile. "Just look at the way he eats up the ground, and he reads the game so well. Scott has got that drive and a fantastic attitude for the game. He is also so incredibly fit, and his athleticism is fantastic. He's one of the best I have seen.
"His passing can get better. But, at 28 now, he is coming into the best years of his career. I really hope they are with us."
Brown concurs with his boss that he is about to enter the peak period of a career which started when he made his first-team debut for Hibs in May, 2003.
Now that the long-term problems he suffered with his hip have finally been resolved, he wants to play in every game.
The Hoops captain said: "I think everyone believes in their own ability, and the best is probably still to come from me.
"I am 28 now, and still have a long career ahead of me. I am enjoying playing at Celtic, and I want to stay here for as long as possible. The main thing is that we are winning things, but we need to start winning more cups now."
Lennon is adamant Brown has to be a front-runner for the Player of the Year awards, and said: "I think he has had a brilliant season, and I would certainly put him down as a contender for Player of the Year."
Voting forms for the PFA Scotland awards went out to players across the country last week.
The Scottish Football Writers' Association members will decide on their top man in May.
Celtic team-mates Kris Commons and Virgil van Dijk will offer strong competition to Brown for the awards.
But Brown is very relaxed about the situation, and is focused only on winning his fourth championship medal since joining Celtic in 2007.
He said of being tipped as a potential Player of the Year: "To be fair, I am not interested in that.
"So long as we get over the line in the league championship, that's the main thing.
"We can then look forward to the Champions League qualifiers again, because it is going to be a huge season for all of us trying to get to the Group Stage."