Lee was 22-year-old when he was picked in the Australia squad for the showpiece tournament held in the Indian sub-continent. The medium-pacer said Warne was "very nice" to him. But Waugh had a theory as to why the leg-spinner forged such a close bond with his young teammate.
"He (Warne) took me in and said, It's gonna be the Shane Show, me and you, the Shane Show'," news.com.au quoted Lee as saying on the latest episode of the Betoota Advocate Podcast.
"And Steve Waugh pulled me aside and goes, How are you going with Warnie?'
"I said, 'Look, he's been really nice to me'. And Waugh goes, 'Mate, do you remember when you were at school and there was a kid at school who had no mates? And this new kid comes to school, and the kid with no mates is all over the new kid?'
"Waugh said, 'You're that new kid and Warnie's the kid with no mates'," Lee, who played 45 ODIs for 48 wickets between 1995 and 2001, added.
Lee also revealed how easily Warne could approach the members of the opposite sex, something which he first witnessed in 1996.
The 46-year-old said during the opening ceremony of the World Cup, every player was accompanied by an Indian model and Warne promised to show him the ropes as the elder statesman of the "Shane Show".
"I was single at the time and Warnie was single on tour," Lee said. "Warnie said, 'I'll get the best two (models) for us -- the Shane Show, the Shane Show'.
"Anyway, he lined up these two girls and we had one drink and we're going back to their place and we're thinking it's all going to happen.
"I said, 'Oh, the Shane Show, really Warnie?' And he goes, 'Don't tell the boys that!'"
"Then we got there and there's her whole extended family there and we spent the whole night signing autographs and having a bloody meal," he added.