Such songs were clearly audible during their defeat by Hearts at Tynecastle last weekend on live television.
Lawwell told the Scotland on Sunday that such behaviour was "unacceptable and offensive", adding that "last Sunday was embarrassing".
Lawwell is determined to rid his club of the remnants of the sectarian problem.
"We have made great strides at Celtic Park and anyone who comes here will not leave with the view that sectarian singing is prevalent," he added.
"You will always have some idiots, but, at Celtic Park, it has reached a margin for error that is difficult to wipe out. The problem is 99% resolved at our home games.
"The issue we have is the away support and songs sung in support of the Provisional IRA.
"They are not overtly sectarian songs, they are political songs that have no place at football. We will be addressing that.
"One of the reasons the away support is still an issue is that it is not within our jurisdiction.
"You need the local police forces and the local stewarding to identify and then police or eject supporters, or identify to us those that are creating the problem.
"We have ideas about how we can co-operate better with the local authorities that we are going to take to them. I do not think it is a massive problem, however."
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