The Saracens prop was part of the 2005 Lions squad that fell to a 3-0 Test whitewash at the hands of New Zealand.
Stevens is currently vying for a place in Saturday's team to face the Barbarians in Hong Kong, before jetting to Australia.
He hopes the tour Down Under will be a more enjoyable experience upon the pitch than that of eight years ago.
"We weren't very successful when I last toured in New Zealand and I'd like to turn that round and be successful this time," said Stevens
"It was a wonderful experience for me at the time because I was so young and I was playing with my heroes. But it was a disappointing tour overall.
"We lost all three Tests which was a huge blow but I did learn a huge amount from it. Having played for England since I know how important it is to be a very tight knit squad and that's one thing Warren is really trying to do.
"The boys are really buying into it and are very open to building firm connections. Everyone is mucking in."
But the former England star, who will battle current Red Rose incumbent Dan Cole and Wales' Adam Jones for a Test spot, is well aware of the challenges the Lions face against Australia.
"It's going to be massively tough," added Stevens. "You're playing across the other side of the world, it's a long trip, you've got to deal with all of that.
"You have to deal with the Aussie team who are a fantastic side and there are a lot of different implications when you're touring.
"There are so many different games - you have the internationals and the midweek games - it's a tough test."