The midfielder has had a big impact on the Hoops' current impressive form since making his return from an ankle injury at the end of November.
The Celtic captain has now been rewarded for his efforts by being named Scottish Premier League player of the month for January.
Lennon said: "I'm delighted for him, I think he deserves it.
"He is playing with great authority on the pitch and he is an excellent captain.
"He has the respect of the players in the dressing room, which is very important to be a captain of a big club. I think he has matured.
"Getting over the ankle injury, I always felt we would get Scott back to his best and now we are seeing Scott at his best.
"People talk about him being a good athlete but he reads the game very well and his football appreciation is good.
"He's a better footballer than a lot of people give him credit for.
"He's really grown into the role and he has certainly galvanised the team since he has come back into the squad fit and healthy."
Asked if he sees similarities between himself as a player and Brown, the manager added: "I do, yes. In terms of personality.
"I think he's got more attributes than I had in terms of his running power and his eye for a goal.
"I'm just very pleased with how he has progressed in the role he has been given.
"He conducts himself very well on the park. His disciplinary record this season is fantastic. I'm not sure how many bookings he's got, if any.
"In terms of his discipline on the park, it's never been an issue for me. He was a little bit hot-headed earlier in his career but we all were.
"He has matured a lot quicker than most people have done. I think he's had to, with the responsibility of the armband.
"He's a tough boy. He's mentally tough, he's physically tough. He's not dirty.
"He gives a few verbals here and there but only when he's provoked. He looks after himself and he looks after his team-mates very, very well."
Celtic face Hearts in the SPL on Wednesday night and Lennon was reluctant to discuss his reported interest in their goalkeeper Marian Kello.
Kello is unlikely to feature against the Hoops after missing the William Hill Scottish Cup tie against St Johnstone at the weekend after clashing with the Hearts board over his refusal to move to Austria Vienna on transfer deadline day.
He was also linked with a move to Parkhead and could quit the Jambos at the end of the season but said on Wednesday he does not want to go to Celtic, where he believes he would not be first choice.
Lennon said: "The window is shut and there is not a story there really. I'm very happy with the three goalkeepers that I've got.
"You are always looking to strengthen but I can't do anything until the summer and, until then, I'm not going to talk about any other player.
"I've had no contact with him and I've had no contact with Hearts regarding the player and I've had no contact with his agent either."
Celtic's last SPL defeat was against Hearts at Tynecastle on October 2, before they embarked on a remarkable unbeaten run.
Looking ahead to this game, Lennon said: "I don't think it gives it any more importance.
"It's the most important game of the season because it's the next one.
"We have a chance to extend our lead at the top of the table and just try to put pressure on everybody else.
"I think we are in a different place to where we were then.
"Confidence is good. The team is playing very well and they are taking a lot of pride in what they are doing at the moment."
Victory would allow Celtic to move four points ahead of Rangers - who are now out of every other competition - and Lennon backed his players to handle any extra pressure which comes their way as a result of their Old Firm rivals' current plight.
He said: "Pressure is pressure. These guys have had the expectation levels for the last few seasons and they are coping very well.
"Whether this brings extra pressure or not, I don't know. But I'm sure it's pressure they can cope with."
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