Supporters across the country, including Celtic supporters groups, have been voicing their concerns over proposals which could see a Rangers newco welcomed into the SPL for the start of next season should the Ibrox side be liquidated.
They have threatened to boycott games with many clubs facing delays in their supporters renewing season tickets until the issue is sorted.
Lawwell, though, has moved to reassure Celtic fans that the Parkhead club are firmly set on keeping the sporting integrity of the Scottish game intact and will do what is best for Celtic and its fans.
Lawwell said: “We are fully aware of our supporters´ concerns regarding the current situation across Scottish football and the breadth of opinion within our supporter base.
“The issues are complex and there is much uncertainty. Indeed, the situation repeatedly changes, even on a daily basis. I am sure our supporters understand that these developments are receiving our full focus and attention.
“Our guiding principle is that we will do what is in the best interests of Celtic Football Club and our supporters, consistent with upholding the interests and reputation of Scottish football.
“I can also give an assurance that we will communicate further and directly with our supporters at the appropriate time.