And while the last of those adventures restored a huge amount of pride in the Lions' jersey thanks to performances on the field and attitudes off it, Warburton insists that anything less than a victory over the Qantas Wallabies won't be deemed good enough.
"For me, no other outcome would be acceptable," said Warburton, who meets up with his Lions team-mates for the first time in London today.
"You only want to go out there for a Test series win. That's what it's all about. Performances are great but it's all about results.
"The answer would be the same for whatever tour you go on - it's the only thing that the players' want to achieve. It's all about the Test series win. It's the be all and end all."
The last lot of Lions to return home having achieved the ultimate goal were Sir Ian McGeechan's class of 1997 after they made a mockery of pre-tour predictions to topple the world champion Springboks in their own backyard.
Warburton was still at primary school when Martin Johnson and co triumphed in South Africa and wasn't even aware of the magic of what was happening in the Republic.
And while plenty of his squad will have fond childhood memories of the day that Jerry Guscott kicked the Lions to series glory in Durban, not a single one of them has yet experienced similar elation with Britain and Ireland's elite.
"A winning Lions tour is something that not one of the players has got on their CV," added Warburton.
"We'll all be desperate to make sure we make every right decision and do everything we possibly can do to get a series win.
"I wasn't watching in '97. I was only nine then and I wasn't really into rugby so much. It was only when I was about 10 or 11 that I started getting into rugby.
"Australia 2001 was the first tour that I really watched, with the likes of (Brian) O'Driscoll, Jason Robinson and I remember Dafydd James scoring a try in the corner. That was my first memory of the British & Irish Lions."