The Scottish champions upset the odds throughout their group campaign, sealing the club's first away win the competition proper against Spartak Moscow, beating Barcelona and then qualifying with victory over the Russians.
Lennon's relatively inexperienced side now face a Juve team, who sit seven points clear in Serie A in their bid to retain the title, with the first leg in Glasgow on February 12. "In this format of the competition, this is the furthest we have been so far," Lennon said. "We would dearly love to go one better. We have two games to have a real crack at it."
He added: "I don't think there is any pressure on us. Yes, the expectation has risen a little bit because we have turned a lot of heads, which we are delighted with. But we have been quietly confident the whole way through this campaign and I see no reason to change that viewpoint now."
Only Scott Brown and Georgios Samaras have played at this stage before and most of Lennon's team are in their debut Champions League campaign.
"They have surprised me with the way they have handled the games, particularly away from home where we have had this hoodoo, or record," the Celtic manager said. "Over the last season and a half they have really improved away from home.
"Hopefully we can take something to Turin, but as long as we are in with a shout going into Turin, then who knows? We will need to play better than we did in Benfica but if we can replicate what we did in Moscow and certainly Barcelona then we will give ourselves a great chance."
Lennon could be without Efe Ambrose for the first leg if the defender reaches the African Nations Cup final with Nigeria in Johannesburg on February 10.
"We will cross that bridge when we come to it and we'll see how Nigeria progress," Lennon said. "Efe is very proud of his nationality and very proud to play for his country.
"It's a big tournament for him and one where he would like to excel for his country. We'll see how Nigeria do but, knowing him, he will play in the final and get on the plane and be ready to play against Juventus. He's just that type."