However, in the wake of Sunday's League Cup semi- final defeat to St Mirren, the Hoops boss has called on his on-field lieutenant to receive the backing he needs from the men alongside him in the trenches.
At Hampden, experienced campaigners did not go above and beyond the way Lennon wanted, and it was left to Brown to try and rally the troops as the flak was flying.
The man who entrusts the 27-year-old with the armband bemoaned the general lack of leadership as their Treble yell was silenced.
But Lennon anticipates his captain will lead his men in a storming bounce back to winning form when they run out against Kilmarnock at Celtic Park tonight.
He said: "On Sunday I thought there was a bit of immaturity in our play at times, players doing their own thing.
"That's not all down to Scott. You want the Wilsons, Mulgrews, Ledleys, the Samaras' to take responsibility for that as well and not leave it all to Scott.
"We have a great captain, but I want more leaders on the pitch."
Lennon has been irked by some of the criticism which has come the way of his team since their shock cup exit.
As the man at whose door the buck stops, he reserves the right to have his say, which he did immediately after Sunday's defeat.
But Lennon does not appreciate others taking what he considers to be cheap shots at his club.
He said: "I read comments from a certain columnist who described us losing the Treble as 'careless', as if winning the Treble is like shelling peas.
"It's a very difficult thing to do, and, as I'm reminded constantly, there are only two managers in the history of the club have done it.
"Some people's expectations are as though we should be decimating everyone. That's not the case.
"But, in my time here, our win percentage is excellent."
Killie boss Kenny Shiels has done more than most to keep that win rate down, sending out his side to defeat Celtic in last season's League Cup final, and winning at Parkhead on their visit there in October.
Lennon respects what his fellow Ulsterman has achieved, but their relationship has taken a down turn since the Hoops boss discovered Shiels has gone on record claiming Celtic underachieved last season.
"That's Kenny's opinion," said Lennon before quickly adding, "It's got nothing to do with him. He should not be commenting on my team or my club. I don't comment on his.
"I don't know what context he is using that in."
Shiels reckons that, by comparison, Killie actually overachieved last year, but Lennon – despite his advice to mind your own business – was happy to offer his own view on that.
"Kilmarnock won the League Cup, then they defended it very poorly, getting knocked out in the first round, which no one seems to touch on.
" I think we've been brilliant and probably overachieved in 2012 for the budget we're working with, the environment we're playing in, the pressure the players are playing under, the analysis that goes with it, and the naivety and youth that is in our squad.
"I think they have performed magnificently and I'm very proud of them."