Barton was one of Rangers boss Mark Warburton’s top targets this summer, and he agreed to move to Ibrox a few weeks ago.
The 33-year-old is a high profile signing for Rangers, and Lennon believes that the midfielder's arrival in Glasgow will increase the profile of the Scottish game.
“Joey will certainly give the journalists a few headlines but it’s all good. That’s important,” he said.
Rangers were promoted back to the Scottish Premiership last season, and they are determined to end Celtic’s reign of dominance.
Celtic have won the last five Scottish Premiership titles, but Rangers should give Brendan Rodgers’ side increased competition next term.
Lennon, who is currently in charge at Hibernian, believes that Rangers’ return can only benefit Scottish Football.
He said: “I think now parity has been restored in the top league with Rangers there is a pizazz back into the game and genuine interest again.
“That comes from having the Old Firm back and it’ll make the league far more attractive to brings players in.
“Going forward at Hibs, we want to become part of that.”
Barton is one of a number of signings that Rangers have brought to Ibrox already this summer.
Warburton’s men have recruited five new players, with Clint Hill, Jordan Rossiter, Matt Crooks and Josh Windass all signing up.