Celtic have long held ambitions to play in a wider arena but they were central in discussions on merging the two Scottish leagues in the summer with the help of a redistribution of funds to second-tier clubs.
In a question and answer session at the club's annual general meeting, Lawwell was asked about the benefits of the Scottish Professional Football League.
"I think the main benefit is that it has given a degree of stability, it's really drawn a line, and it's given us something new," said Lawwell, who was re-elected unanimously to the board along with majority shareholder Dermot Desmond.
"Another major benefit was the redistribution of finance from the top league going down to the lower leagues which I think was a great show of solidarity for Scottish football. Hopefully that will give its benefits in terms of the quality that will be in the new Championship.
"I think the line is drawn now so we know where we are, but it's not the end. Everyone in Scottish football has got to look at the challenges that face them and come up with a strategic plan that will maximise the potential of Scottish football going forward."
When asked if Celtic would continue to explore other avenues, he said: "Yes I think we have a duty to do that, not just for Celtic but for Scottish football. The way the world has gone in terms of media values, which are driving the success of major leagues around the world, in a country of five million people it is very difficult to bridge that gap.
"So I think we all have a responsibility to continually look at the playing environment in Europe and make sure that if there is change, and I think there will be change in the coming years, that Celtic and Scottish football play a part in that."
The SPFL recently signed a deal with a Chinese online TV station, which forms part of a 10-year agreement which is expected to bring in £2million a year for the clubs and Lawwell is eager to explore further opportunities in the Far East.
Lawwell said: "We're looking at possibly partnerships around academies, we're looking at partnerships around player development and possibly social projects over there so in the longer term the Celtic brand, if you like, gets profile and exposure, not only in China but other markets."
Chairman Ian Bankier declared even more ambitious goals on the international arena.
Bankier said: "I would love to see this club become one of the main players on the world stage of modern football.
"I think there is tremendous romance and expectation about Celtic Football Club. I think we put smiles on people's faces everywhere and in every continent of the world.
"I think we have a tremendous attitude to life, I think we have humour, I think we have a sense of social responsibility, I think we have great people in here, I think we have the best fans in the world bar none and I think the combination of that is unstoppable.
"I think the momentum that we have built over the last three to five years is powerful. I think if we get lady luck on our side and we meet with more success on the field, because it is all about football success, if we can do that and continue the way we are going we will be nothing short of unstoppable."
Meanwhile, Lawwell revealed he was still awaiting responses from the authorities after making an application to Glasgow City Council to develop a safe standing area at Celtic Park.
- Sports & Recreation
- Celtic Football Club
- Scottish football