Brown lift the Scottish Premiership trophy following Sunday's home game against Dundee United.
The Hoops clinched their third successive title at Partick Thistle in March but have had to wait for the silverware until the last game of the campaign.
The Celtic boss, though, insists it will be worthwhile when the traditional podium celebrations take place in front of what will be a huge crowd at Parkhead.
"We have been a long time waiting on it, seven or eight games," Lennon said. "We didn't get the opportunity to celebrate it properly with our own supporters but on Sunday we can.
"Obviously we have a game first and that will take centre stage. But there is no better feeling as a manager than seeing your captain lift the championship trophy.
"It is the third one in an row and I am really looking forward to it.
"I know our players will want to finish the season on a high and get 100 goals and we are only one away, which is brilliant.
"We have won five and drawn two since we won the championship and that is excellent, keeping our focus when we are so far ahead, which is a difficult thing to do.
"There is no pressure on Dundee United either, and they play good football, so we are hoping it will be a good game of football. We will go as strong as we can."
Celtic have only lost to Aberdeen in the league so far this season but it is the home William Hill Scottish Cup defeat to the Dons that irks the former Hoops skipper more.
"It (league defeat) doesn't blot what was a fantastic campaign," Lennon said.
"The cup defeat annoyed me but I can count on two fingers the amount of games I have been upset by players domestically this season.
"They have been fantastic. They get taken for granted. There is an expectation that they should just go out and streamroller teams and that is being disrespectful to the opposition.
"But over the piece, we have played some brilliant football and I don't think too many people can complain about their performances this year.
"We had 79 points last year, we are on 96 at the minute and can get to 99 so I think that is a huge improvement in the league."
With another title win comes another tilt at the Champions League and Lennon will look to play a friendly at Murrayfield in preparation for the first qualifier in July.
Celtic Park is out of commission due to the Commonwealth Games, with the home of Scottish Rugby in Edinburgh the only suitable alternative.
He said: "That is maybe something that we have to look at, just to get used to the pitch and the dynamics for the stadium, or maybe even some training sessions on it."
Before that, the Northern Irishman will spend a week at the World Cup in Brazil as a pundit for the BBC where he may, depending on call-ups and selection, see some of his own players such as Emilio Izaguirre (Honduras), Efe Ambrose (Nigeria), Georgios Samaras (Greece) and Fraser Forster (England) in action.
"It is fantastic," Lennon said. "I think it is characteristic of the way we have improved over the last few years.
"We have four, maybe five, representing us at the World Cup, I think it is great for the reputation of the club and that can only enhance our chances of bringing other players here, if those players do well."