He was speaking following the release of Celtic's interim financial results on Monday which he described as "very satisfactory".
The possible demise of the club altogether has also been raised in the media, leading to questions over Rangers' historical relationship with Old Firm rivals Celtic and the very future of the game in Scotland.
However, Lawwell was unequivocal when he told Press Association Sport: "The way we would look at is we don't need Rangers.
"We have a strategy that we have embarked on, that's independent of Rangers or any other club in Scotland.
"We have a vision, horizons and aspirations which are in Scotland and beyond that, in terms of European progression.
"So that's what we are focusing on.
"In terms of Rangers' situation at the moment, nobody really knows what the facts are.
"I think it is inappropriate for us to comment on it.
"We are getting on with it, we are independent in terms of where we want to take the club and that's what we will continue to do.
"These are challenging times at the moment and we have to face them. There is a lot of big thinking to go on.
"In term of ourselves, we have set out a strategy which is now beginning to produce for us.
"Five years ago we said that we could no longer compete at the highest level, we could no longer attract the Premier League players that we had done, so we invested a lot of money in our recruitment and academy and creating, hopefully, a centre of excellence with the tentacles going far and wide.
"Identifying uncut diamonds, bringing them here, developing them and putting them in the team.
"We are beginning to see that with the strength and the value of the squad and the academy kids who are pushing to come through. So that is satisfying."
Asked if Scottish football could survive and thrive without Rangers, Lawwell replied: "If people take some clues from what we are doing, then why not?
"Again, I think it needs big thinkers. It needs people to think outside the box."
Looking at the situation FTD's managing Director George Moss commented:
'The problem as I see it for the SPL as a whole would be the loss of potential TV revenue to smaller clubs with the 'Big Two' being featured far more times on the road than any other teams. In the long term that could have a knock on effect for things like sponsorship values and media rights. As far fetched as it is if Rangers went out of existence there is bound to be less media interest and probably coverage.'
'Celtic may well do well whatever their neighbours plight - it would certainly open the way for automatic Champions League football and there's a danger a larger financial gulf will emerge between the clubs. But, that has been the case in Manchester for over 20 years until the last two or three and United have thrived as City have floundered.'