Dawson was with McGeechan on the victorious 1997 Lions tour to South Africa and also knew him as a player as both Northampton Saints and London Wasps. And in the eyes of the English 2003 World Cup winner, there has been no greater Lion than his former coaching mentor.
"There have been many great players associated with the Lions over the years, with names like Willie John McBride, Martin Johnson, Scott Gibbs and Gareth Edwards springing to mind," Dawson told BBC's 5 Live.
"But as someone who embodies everything it is to be a Lion, there is nobody who will come close to what Geech has brought to the red jersey.
"From player, to coach, to manager - not to mention assistant manager and consultant - he epitomises the Lions as a brand and as a team.
"He laughed when I asked to speak to Sir Ian when I phoned to congratulate him on his knighthood, an embarrassing giggle of disbelief. I can imagine him opening his post, just like any other person, and being completely gobsmacked to read the letter when the news came through.
"I can picture his wife Judy asking what's wrong and him showing her the letter; and I can almost see the sheer disbelief on their faces - but it makes perfect sense.
"That's one of the reasons why everyone thinks he deserves the honour: his humility and his under-the-radar dedication to be successful on behalf of the teams he has worked for. I'm very proud to know him and I know that, despite the knighthood, he will be exactly the same as he always has been.
"I first met Geech in 1995 when he was thinking about coming to coach at Northampton - and he hasn't changed.
"He was very quiet and thorough in his preparation, but always so positive and incredibly knowledgeable. And he had an ability to communicate with his players in a way which always made them perform to their best.
"He has an empathy with players - not because he played at the highest level but because he has this ability to understand what the players are going through. As a coach, he has developed and changed in the 14 years I have known him, which marks the quality of the man.
"He appreciates the game has moved on - the skills he had in 1995 were very different to what he took with the Lions in 2009. But he still manages to bring quality to the table.
"For everything he achieved with Northampton, Wasps and Scotland, it really is the Lions where he really marked himself out as a legend. On Lions tours there is so much tradition and history, you have to be aware of what it means to put that red jersey on.
"But when Geech spoke, you didn't just feel like you were flicking through history books reading about JPR Williams, Willie John McBride or Gareth Edwards - you felt like you were sitting next to them. Geech's words brought the whole thing alive.
"You weren't just a 1997 or 2009 Lion: you were a Lion. You felt two inches taller, two inches wider and two paces quicker: not only did you not want to let your own team down, but you didn't want to let the Lions "brand" down. Geech fully understood that.
"With the Lions, relationships are not just built on the rugby field - it is imperative to get it right off the field. Other coaches have failed miserably and overlooked the social aspect. But Geech never did - you only need to look at the players from the 2009 tour and see how well they played.
"There would be plenty of coaches who wouldn't participate with the players' Court. Geech would and could be one of the lads, but he knew where the line was and never overstepped it.
"I can't remember an angry word from him - he always had an angry sidekick like Jim Telfer, Warren Gatland or Shaun Edwards.
"Those players who went to South Africa in 2009 will tell you that if they bumped into one of their fellow Lions, they would give them an enormous embrace because there is a bond that will be there forever.
"And that's because of Geech - the ultimate Lion."
IAN McGEECHAN - THE ULTIMATE LION
IAN McGEECHAN - Born: 30 October, 1946 - Leeds, England
Ian McGeechan was appointed Head Coach for the 2009 British & Irish Lions tour to South Africa on 14 May, 2008 - his fifth tour as a coach and his seventh overall with the Lions. He also toured South Africa in 1974 (four Tests) and New Zealand in 1977 (four Tests) as a player and therefore surpassed the legendary Willie John McBride in 2009, who went on five tours as a player and one as a manager.
His role as Head Coach in South Africa was his fourth in that capacity following trips to Australia in 1989, New Zealand in 1993 and South Africa in 1997 . He was the Midweek Coach on the 2005 tour.
As a player, he played for Headingley and made his debut for Scotland in 1972. He won 32 caps, playing at outside-half and centre, and captained Scotland in nine Tests. In 1986 he became assistant Scotland coach and in 1988 was promoted to coach. In 1990, Scotland won the Grand Slam.
In 1994 he was appointed Director of Rugby at Northampton Saints and in 1999 he became Scotland's Director of Rugby.
In 2005 he took over as Director of Rugby at London Wasps and in his first season he guided his new team to the Powergen Anglo-Welsh Cup and followed that up with the Heineken Cup in 2007 and the Guinness Premiership title in 2008.
IAN McGEECHAN WITH THE LIONS
AS A PLAYER
1974 South Africa P14 W13 D1 L0
Lions played 22 games
1977 New Zealand* P16 W11 D0 L5
Lions played 26 games
Overall P30 W24 D1 L5
Overall Tests P8 W 4 D1 L3
AS HEAD COACH
1989 Australia P12 W11 D0 L1
1993 New Zealand P13 W 7 D0 L6
1997 South Africa P13 W11 D0 L2
2009 South Africa P10 W 7 D1 L2
Overall P48 W36 D1 L11
Overall Tests P12 W 6 D0 L6
AS MIDWEEK COACH
2005 New Zealand* P12 W 7 D1 L4
Overall Coaching P60 W43 D2 L15
Overall Lions P90 W67 D3 L20
* 1977 includes game v Fiji
* 2005 includes game against Argentina