Speaking at Friday's AGM at Celtic Park, Lawwell warned fans they were putting the club's reputation at risk.
Lothian and Borders Police confirmed they had launched an investigation into allegations of the "singing of sectarian songs" following Celtic's 2-0 defeat by Hearts on October 2.
Lawwell said: "Chants glorifying the Provisional IRA are totally unacceptable.
"One, it is wrong, and it is an embarrassment to the club and embarrassment to the majority of supporters.
"We were inundated by complaints from our own fans after the game at Tynecastle.
"We have dealt with it at Celtic Park and we will do all we can to make sure it doesn't happen home or away.
"We don't want it, we don't need it.
"We have the best supporters in the world and hold that reputation dear."