The 34-year-old centre was a member of the 2001 squad that led 1-0 in the series before they were overhauled by the John Eales-captained Wallabies.
O'Driscoll, one of only three Lions players in their 125-year history to have been on four tours, tasted further disappointment in New Zealand in 2005 and South Africa in 2009.
"These players, I think they're desperate and want to be part of a successful Lions tour having not done that," Gatland told reporters.
"I spoke to Brian at training this morning. He said he's a little bit worried having come out here as a young 21-year-old and having been a part of a series that was close and just losing.
"He's sort of on the cusp of this being his last chance to be a part of a winning Lions series.
"He's desperate, he wants to be able to communicate that to the players to say, 'don't leave this opportunity behind' because it can quickly be that you don't get that chance again.
"So, 'don't waste the moment' is the message that's gone into this."
The Lions find themselves in a similar position to the 2001 tourists, heading into Melbourne with a 1-0 lead after winning the opening Test in Brisbane and with the prize of a first series win since 1997 tantalisingly close.
Gatland will rely on another old Irish hand in the backline in 29-year-old Tommy Bowe, who made a quick recovery from a broken hand to dislodge Alex Cuthbert from the starting 15, despite the Welsh flyer scoring a try in the opener at Lang Park last week.
Gatland said Bowe, capped 51 times for Ireland and one of five changes to the Lions starting side from the first Test, was a "massive" big-game player.
"One thing you can't do is you can't coach experience and experienced players come in and are able to slot in really quickly," the New Zealander added.
"And he did that on Tuesday morning. You could see the experience and quality that was there and I think that will give a boost to some of the other players."
A sell-out crowd of more than 50,000 will pack out Docklands on Saturday, with the expectations of a huge contingent of red-shirted tourists to lend a frenetic atmosphere under the stadium's closed roof.
Gatland said his players were well aware of the weight of history and the hopes of Lions fans desperate for a first series win after 16 years, but wouldn't want to ponder it too much in their final preparations.
"It can't consume us and it's important that it doesn't do that because we've got to be able to go out there and be mentally strong," he added.
"If that weight of expectation is too heavy, sometimes that can sort of - you can go into your shell a bit, it can constrict your play.
"So we've got to make sure we get the balance right between identifying that, talking about that, but also giving the players a freedom to go out there and play and express themselves and win this Test series."