Tickets for eight of the nine matches were up for grabs on Monday with the games against the Wallabies in Sydney and Melbourne selling out in 15 minutes and the opening Test in Brisbane following suit after just five minutes.
The allocation for the tour match against New South Wales Waratahs at the Sydney Football Stadium was also sold out, leaving only tickets for the tour matches in Perth, Brisbane, Newcastle, Canberra and Melbourne up for grabs.
"To see allocations exhausted for the three Test matches and for the Lions match against the Waratahs is a wonderful endorsement for what will be a truly memorable visit by one of international sports' most iconic teams," ARU chief Bill Pulver said.
"Twelve years ago there were 300,000 tickets sold for the nine matches.
"In 2013 we are hopefully on track to reach close to overall attendance numbers of 400,000 for the same number of games."
The Lions, who tour every four years alternating between South Africa, New Zealand and Australia, stop off to play the Barbarians in Hong Kong on June 1 before beginning the tour proper against Western Force in Perth four days later.
Tickets for the three Tests were already up for sale at vastly inflated prices on websites on Tuesday, despite ARU warnings about such tickets being subject to cancellation without a refund.
Two tickets for the opening Test in Brisbane with a face value of A$235 were being offered for A$1,285 the pair on eBay.