The Parkhead chief executive was speaking following the release of Celtic's interim financial results today which he described as "very satisfactory".

Lawwell, though, is aware that it is Rangers' finances which are under intense scrutiny at the moment.

The ailing Ibrox club today filed legal papers with the Court of Session in Edinburgh signalling their intention to enter administration, as they await the verdict of a tax tribunal.

The HMRC case centres around the use of employee benefits trusts (EBTs) which were in place before Craig Whyte took over as chairman from Sir David Murray last May, with Rangers looking at a possible bill of around £49million.

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."

One of the many scenarios being talked about in the event of Rangers folding is the prospect of a phoenix Rangers Football Club emerging and being invited to go straight into the Clydesdale Bank Premier League, on the strength of broadcasters' interest in covering Old Firm games.

Rangers supporters, though, might take little succour from Lawwell's cryptic response to that possibility.

"I think it would be inappropriate for us to comment on that," he said.

"We would have some strong views around it, but to be shared at that time.

"Nobody knows (what is going to happen). There has to be closure on all of this.

"Closure on Hearts, closure on Rangers, or any other club out there so there is a certainty and stability brought in."

Lawwell expanded on his thoughts about the future of Celtic when asked if the fans would continue to support the club in the same numbers in the absence of the Old Firm rivalry, a mainstay of the Scottish game for well over a century.

"Absolutely," Lawwell said. "It is a changing world.

"Nothing stays the same and our job is to make sure we are still seen as a big important club in Europe and if there is any change we are part of that."

As for the potential for a European League, Lawwell said: "Who could say? Possible, or a extension to the Champions League or an extension to the Europa League.

"That's where we are with it all. We are looking long term.

"I think we are doing all the right things, in saying that, we are still to win (the league), we are not getting carried away or gloating or getting ahead of ourselves.

"We know what we have to do, we have to deliver and then hopefully this long-term strategy keeps the fans coming, keeps them interested and connected with Celtic.

"And I think they have, Neil (Lennon) has done that and season books are up this year."

Celtic reduced their bank debt by £2million during the second half of last year, with turnover increased by 3.1% to £29.3million.

The club made a pre-tax profit of about £180,000 while cutting the debt to just over £7million, a figure chairman Ian Bankier described as "very manageable number" among a "robust" set of figures.