The Hoops won the Scottish Premier League and the Scottish Cup while also enjoying a successful run in the Champions League.
However, Commons admits that Lennon will be eager for the team to push on during the new campaign.
"We will all be sitting down within the next week or so and discussing how we can at least emulate the last campaign or do better," the Scotland international is quoted as saying by Sky Sports News.
"You can be sure he will want us to win the treble and, at least, get into the last 16 of the Champions League. He demands that we improve every year and will not let us stand still."
Celtic start the defence of their SPL title at home to Ross County on August 3.