The pressure on the Celtic boss intensified after the 2-2 draw with Livingston on Wednesday night left the Parkhead side without a win in four matches and 20 points behind Rangers in the Scottish Premiership title race.
But Caldwell, who won the title as Lennon’s team-mate in 2006-07, believes the problems at Parkhead go "deeper" than the under-fire Northern Irishman, and that the club's "obsession" with 10-in-a-row has been a factor in their failings.
"He's under a lot of pressure, as any manager would be if you're not winning football matches," Caldwell told Sky Sports News.
"He understands at Celtic more than anyone you have to win games as the manager of the club, but I think it runs a little bit deeper than Neil Lennon.
"Has recruitment been right? Is the style of play right? Is everyone behind the scenes pulling in the same direction?
"For me there's been an obsession with 10-in-a-row that has forced Celtic as a football club to forget the processes that allowed them to win leagues and win cups and that's what's cost them this season.
"As a manager of any football club, but Celtic even more so, you're judged by results and you have to win games. But as a football club you have to look at the bigger picture and decide whether the manager is aligning to what the club's values and beliefs are, where the club is going, and if Celtic believe Neil Lennon is that man then they will continue to go with him.
"If they don't believe that then that's why it should change. I don't think you should change manager purely based on results on the pitch."
Caldwell also gave his opinion on Scott Brown’s red card five minutes after appearing as a substitute in the 2-2 draw at Livingston.
"I think he was a little bit unlucky,” he said. “I don't think there was lot of intent in it and he’s caught him with his arm.
“It's just the way it’s going for Celtic at the moment. It's one disaster after another.”