Celtic clinched their third consecutive title with seven matches to spare on Wednesday night when a 5-1 victory over Partick Thistle left them with a 26-point lead over Aberdeen.
With Rangers still experiencing financial difficulties ahead of their move into the second tier of the Scottish game, Celtic fans are predicting their run will stretch to a record 10 titles in a row.
And Lawwell admits there needs to be change.
"There are challenges ahead in terms of creating meaningful games," he told Sky Sports News. "No question, that is one of the challenges that Scottish football faces.
"I think we are realising that as a nation and we need to find some form of solution."
Lawwell knows he might also face a fight to hold on to manager Neil Lennon following the comfortable title win.
"The consequence of success is that people become intrigued with our manager, your coaches, your scouts, and then eventually maybe court them," he said.
"Neil, I think, is a big part of Celtic and Celtic is a big part of him. I think it would be a wrench for Neil to leave, however he is an ambitious guy, a highly-talented guy, and through time who knows? But hopefully we can provide the motivation and context for him to stay here."