The Hoops wrapped up their third successive crown - the quickest championship victory in 85 years - with a 5-1 drubbing of Partick Thistle with seven games of the campaign remaining.
In recent seasons the club has pulled in millions by moving on a number of players including Ki sung-Yueng, Victor Wanyama, Gary Hooper and Kelvin Wilson.
Of the current crop, keeper Fraser Forster, who has conceded just 15 goals all season, and central defensive duo Virgil van Dijk and Efe Ambrose, have been linked with big-money moves to England.
But Lawwell believes the prudent nature which the club has gone about its business in recent years means they could cope without participating in Europe's elite competition, although he admits it remains their major target for the summer.
Speaking to Sky Sports News, he said: "We have a good foundation at the club and there is no real necessity to sell players now.
"Having won the championship our focus is to step up the summer planning we have had in place for the past couple of months. We need to plan for the summer, plan for the qualifiers and hope to get through, but we do not have to sell players."
And Lawwell is confident manager Neil Lennon will remain in charge of the club and lead their quest for a third successive season of Champions League football.
Lennon has been linked with the managerial vacancy at Nottingham Forest but Lawwell is convinced the Irishman's love affair with the club will continue for many seasons to come.
Commenting on those reports earlier this week, Lennon revealed he valued his relationship with Lawwell, and the Celtic board, and enjoyed the freedom to carry out his job without interference.
"The true consequences of success is that people will become intrigued with your manager, your coaches, your scouts... and then eventually may court them," said Lawwell.
"Neil is a big part of Celtic and Celtic a big part of him and from my point of view I think it would be a wrench for him to leave.
"However, he is an ambitious guy, he's a highly-talented guy and through time who knows? But hopefully we can provide the motivation and context for him to stay here."
But former Celtic striker and Sky Sports pundit Charlie Nicholas believes Lawwell may be unable to reject advances for his manager, and his players, should the right circumstances prevail.
Speaking to Sky Sports News he said: "Peter can say what he likes, and play the Celtic party politics, but the facts are simple, if a good offer comes in for any of his players he sells.
"He sold Wanyama, who was his best midfield player and he sold Hooper, who was his best striker. You can dress it up and say the players want to play in the Premier League but because they don't have to sell doesn't mean they won't sell.
"And no matter what Peter Lawwell says, if there is any significant offers come in for their manager that is the biggest key of all for Celtic.
"I don't have inside information at Celtic - we don't always see eye-to-eye - but my opinion is that if a genuine offer came in for Neil, Garry Parker and Johann Mjallby, who as a group are very, very good, he would probably give it major consideration."