The Parkhead side head to Amsterdam next Wednesday night to take on Ajax and a victory would go a substantial way to keep the dream of a second-placed finish to progress from Group H.
Finishing third and dropping into the Europa League would give Celtic a better chance of a prolonged run in Europe beyond Christmas, compared to the stiff test in the Champions League.
And Lawwell admits he would rather the Hoops take their chances against the big boys in the last 16 than go on a money-spinning run to the latter stages of the lesser competition.
He said: "There is an argument there to say that we could do well financially from going into the Europa League, no question about that.
"But the prime objective here isn't one of commercial gain, it is a sporting one.
"We want to be the best on the field that we can be and we want to give our supporters the very best.
"So the prime ambition in the Champions League will always be to try and get out of the group and into the last 16.
"There could maybe be a better chance of winning a European trophy if we were in the Europa League, but I would still say that for us as a club, we want to be in among the best and that is what the Champions League is all about.
"Getting out of this season's group is still the main aim for Neil and the team."
Lawwell, meanwhile, has no concerns the travelling Celtic fans will face any hassle in Amsterdam after trouble in the away end in the first leg at Parkhead.
"It was a minority out of 2,800 people here who unfortunately behaved in a manner that nobody would like," he said.
"Our fans travel really well, there's a lot going, more than who have tickets, and we have taken all the precautions, because the relationship is so good with Ajax, to make sure that it goes smoothly."