The Scotland international has had a stop-start campaign due to a hip injury which has seen him sidelined for most league games so far.
But the Celtic skipper was in fine form as he led his side to a goalless draw against Portuguese side Benfica on Wednesday in their opening Group G Champions League match.
Brown was the only player in the Hoops side with any experience of Europe's elite club competition and Lennon praised him for leading by example in the match.
The Celtic manager, whose side sit a surprising fifth in the league, hopes to have his influential captain available for the home match against Dundee on Saturday as the Hoops aim to get back to winning ways following a disappointing defeat to St Johnstone in their previous league fixture.
"He just gives the team real drive," Lennon said. "There were moments in the second half against Benfica when he saw the danger coming and he covered the ground quickly to make tremendous tackles.
"He stopped the majority of Benfica's counter attacks by nipping them in the bud quickly. He's improving all the time. He has matured a lot since coming to the club, taken the captaincy and blossomed into the skipper he is.
"He's one of our more experienced players who has played at this level before. We had 10 players out there who hadn't played in the Champions League before the game against Benfica. He sets the example for the rest of them.
"But there were so many pluses for the team. However, I thought Brown in the second half was colossal.
"We may have to be careful with his injury but he recovered quickly from the game at the weekend which was pleasing.
"He also finished the game tremendously strong which was surprising considering the condition he's had. We'll now have to see how he is over the next couple of days."
The visitors to Celtic Park on Saturday are Dundee, who took the place of Rangers in the top flight after the Glasgow side were demoted to Division Three.
They have taken just four points from their opening six fixtures but defender Gary Irvine says the Dundee players can use St Johnstone's defeat of Celtic to inspire them to victory over the Hoops.
"It was good to see St Johnstone getting points. It gives us a wee bit of confidence going into the game but in the same breath I'm sure it gives them a massive kick up the backside," Irvine said.
"But it's just been an example of how unusual the start of the season has been. With Rangers out of the league, I don't think anybody looked ahead of what was going to happen.
"It was all about what was happening elsewhere so I suppose the fact that they have missed out on a few points gives all the other teams a glimmer of hope.
"Beating the champions is never easy but they did it, so it's certainly possible."
Ross County will hope they can continue their unbeaten start to the season when they welcome St Johnstone to Victoria Park while second placed Hibernian welcome Inverness Caledonian Thistle to Easter Road.
On Sunday, league leaders Motherwell are away to Aberdeen.
Fixtures (1400 GMTunless otherwise stated)
Saturday
Celtic v Dundee, Dundee United v Hearts, Hibernian v Inverness CT, Kilmarnock v St Mirren, Ross County v St Johnstone
Sunday
Aberdeen v Motherwell (1145)
Source: AFP
Source: AFP