The giant second row has hardly played this season having been sidelined with a back injury but, rather than detract from his captaincy credentials, Lynagh reckons his 'freshness' is just what Warren Gatland and co need against the Wallabies.
"I guess the favourite is (Sam) Warburton, but for me it has to be Paul O'Connell," said Lynagh, at the launch of Specsavers' sponsorship of match officials for the 125th anniversary tour.
"He's done it before, he's a big guy, an inspirational bloke. He's fresh because he hasn't played much this season and is as fit as he's ever been.
"From a political point of view you have Scottish, Welsh and English represented in the management and no Irish. Appointing O'Connell would balance things up.
"I'd go down the 'tour captain' route because it takes the pressure off who's going to be a certainty in the (Test) team.
"If he's not playing well, do you drop the captain? If you pick a tour captain then he has to perform during the opening three weeks of the tour to get in the Test team. That would be interesting."