The Lions have won a Test series against the All Blacks just once before in 1971 and it is regarded as the toughest of all destinations.
McGeechan has first-hand experience of trying to unseat the Kiwis in their own back yard after taking charge of the 1993 Lions, who were defeated 2-1 by Sean Fitzpatrick and co.
He also travelled there as a player and coach with Scotland, giving him a unique insight into the challenge awaiting Woodward's 44-strong party Down Under.
"Rugby and the Lions are so important to New Zealanders. It had a huge impact on me as a player when I went there for the first time, and then as a coach," he said.
"As you spend more time there you get a better understanding of the thinking of what makes an All Black. It's quite unique in the way their players come through.
"When you're there, you're not just taking on the All Blacks, but the whole country. In four tours, I've had one Test win as a player and two as a coach so I know how hard it is.
"To win a Test series in New Zealand is a high point in anyone's career because it doesn't happen very often. It's great to win a Test there, never mind a series."