Rangers won promotion from the Scottish Championship last season to set up semi-regular league fixtures against their bitter Glasgow rivals.
It is a mouth-watering fixture in itself, but the Gers' acquisition of the outspoken midfielder has certainly added to the intrigue as both sets of fans relish the subplot of Barton versus Brown this season.
The 33-year-old midfielder was not in Glasgow long when he claimed to be in another league to the Celtic skipper as far as footballing ability goes, before then taking aim at Hoops boss Brendan Rodgers over a lack of major honours on his CV.
Lennon managed Brown at Celtic for four years and claims the 30-year-old will get the better of the Rangers man in athleticism, pace and power, though admits that the former Newcastle United and Burnley ace may be better technically.
"He [Brown] has certainly got the athleticism, the power, pace. He'll certainly dominate Joey in that department. I think Joey's technically, probably slightly better," he told BBC Sport.
"I didn't think he [Brown] had a great season last year but I think that was down to injury. I watched him last Sunday against Hearts. I thought he was back to his best."
The first Celtic - Rangers meeting of the season comes at Parkhead on September 10.