But the 2001 tour escaped him: not because he was overlooked, but because he chose to step aside.
Having masterminded a stunning series triumph over South Africa four years earlier, McGeechan was the heavy favourite to be handed the role Down Under. But the vastly experienced465f Scot decided not to put himself forward, leaving the door open for Graham Henry to become the first foreign coach in Lions history.
The Lions went on to run the World Champion Wallabies close, but not close enough as they fell just short in a remarkable three-match series.
The tourists produced some stunning rugby but much criticism headed Henry's way for his perceived heavy-handed training methods, while individual players such as England's Matt Dawson and Austin Healey were hounded for disruptive and unnecessary comments they made to the media.
But while hoards of armchair critics looked for one big reason why the Lions left for home empty handed, the man who knows the world's most-famoustouring team better than anyone else took a far more measured approach.
"So why did we lose?"McGeechan asked in his column in Rugby World in September 2001.
"In short, because we did some little things less well than Australia.
"The Sydney Test was nip and tuck, but we made one or two rash decisions, we didn't get out of our 22 when we should have done, we didn't score when they were down to 14 men.
"Matt Burke nailed two tricky kicks while Jonny Wilkinson missed two - it's differences like this that cost the Lions the series.
"But ultimately we lost the series in Melbourne because the Wallabies were on the ropes with nowhere to go; we didn't land the killer blow and they gained confidence from our mistakes."
Sir Ian McGeechan believes injury to Richard Hill had a massive impact in 2001
McGeechan, who was a series winner with the Lions on their most-recent tour to Australia prior to 2001, highlighted the loss of a future England World Cup winner as the key moment when the tide turned in favour of the Wallabies.
The Lions had been in control for the vast majority of the opening Test and the first half of the second a week later, but that all changed when they lost a central figure at the half-way point of the series.
When Australian centre Nathan Grey caught Lions flanker Richard Hill on the chin late in the first period, four nations held their breath. The Saracens star finally got back to his feet, but he was dazed and confused and seemed to have no idea where he was.
They don't come any braver than Hill and if anyone could recover quickly it would surely be him. But it wasn't to be. By the time the teams came out for the second period, Hill wasn't among them.
The Lions collapsed without him, slipping to a heavy defeat in the remainder of that match before failing to win the decider without their inspirational back rower a week later.
For McGeechan, Hill's misfortune and disappointment wasn't just personal - it lessened the confidence and effectiveness of a squad full of hugely-talented individuals who had little left to give at the end of a gruelling campaign.
"I'm disappointed the 2001 squad didn't win the series and can't help feeling they threw it away," added McGeechan, who selected Hill for all three Tests against the Springboks in 1997.
"They had the better of four of the six halves of Test rugby, but the 15 points they conceded in the seven minutes after half-time in Melbourne decided the series.
"Richard Hill went off with concussion at half-time in that game and his absence thereafter probably cost the Lions the series - that's how influential he is.
"Hill was one of my players of the tour. Another was Johnson, whose presence was again enormous. In the backs, Jason Robinson was outstanding. Brian O'Driscoll was another to relish the company he was in and I think the Australians were surprised by the ability of the Lions backs one on one.
"Martin Johnson said that by the end of the Lions tour the squad were running on empty and were held together by sticky tape. He is the last player to look for excuses, so for him to say that shows there is a lot of credence to his words.
"Quite simply, the Lions were at breaking point - both physically and mentally."