Evergreen Wales star Williams has figured on two previous Lions tours but saw his dream of success snatched away by Australia and New Zealand.
But the flanker promises he's more driven than ever and has his sights set on making it third time lucky against South Africa this summer.
Williams, 33, said: "Getting selected for the Lions is the ultimate for a rugby player and I'd be lying if I said I didn't have an eye on it already - I would love to go again.
"It's a huge achievement to be selected and it's a great experience. I really enjoyed the last two tours but they both ended in defeat.
"To win one separates you from the rest and it's one thing that is missing from my CV. I hope I can stay injury-free because I would love to finally be part of a winning Lions side."
Williams was a member of the 2001 and the 2005 series down under and he eventually made his long-awaited Lions debut in the Third Test against the All Blacks at Eden Park.
And he insists the tours have only wetted his appetite for more and bid to eclipse the stunning series triumph of coach Ian McGeechan's men against the Springboks 12 years ago.
"Any player around the four home countries international set-up at the moment will have an eye on the Lions tour," he said.
"It will be a huge challenge but we've got the players in the British Isles to do well.
"I remember picking up Neil Jenkins from the airport after the 1997 tour and he was buzzing. I'd watched the games on television and it really captured the imagination of the public.
"It really kick-started the Lions again because there hasn't been many successful years in recent history.
"All the Welsh lads like Neil, Rob Howley, Dai Young and Scott Quinnell said it was the greatest experience of their careers and hopefully we can learn from them."