"If I can achieve half of what JPR did I would be really happy," said the 28-year-old Osprey.
"JPR and Scott are from the same Bridgend area as I live in. I also train at the same gym as Scott.
"They were a couple of Lions legends and hopefully I will come back and put my name alongside those players."
Fellow full-back Williams was hailed a Lions great following the invincible 3-0 tour of South Africa in '74 while powerhouse centre Gibbs was named man of the series in the 2-1 triumph 12 years ago.
And Byrne reckons the current crop will prove the doubters wrong and beat the bookies' favourites.
"I'm just concentrating on getting out to South Africa and winning the Test series. I can't wait to get out there.
"The composition of the squad is really strong and there's a nice mix. We've got talented Welsh, Irish, English and Scottish players and I'm looking forward to playing alongside them.
"We've got a great chance of winning the series and creating even more Lions history. It would be great to be part of something special - we can definitely do it."