The 72-year-old went on to coach his country against the Lions three decades later but tasted defeat in heart-breaking circumstances to a Sir Ian McGeechan inspired outfit that lost the first rubber but won the second and third.
"A Lions team arriving is exciting, just because it doesn't happen very often," Dwyer told BBC Sport.
"It is a unique international team in bringing together a number of other national sides - there is no other team that does that.
"It has a certain sort of romance about it. I have been enthralled ever since watching the 1959 tourists practice as an 18-year-old and have been a massive admirer of them ever since.
"If there is pressure as hosts it is because Lions tours are so infrequent that it is a long time, beyond most players' individual careers, to square the account if you lose."
Dwyer never had the chance to 'square the account' after the disappointment of defeat in 1989 but he did face the Lions in a non-Test fixture 12 years ago.
The ex-Leicester and Bristol boss was in charge of the Waratahs for their controversial clash with Graham Henry's side in 2001 - a game that became infamous for Duncan McRae's attack on Ronan O'Gara but ended in another loss for Dwyer.
His countrymen can out on top in the Test series last time out, though, and Dywer is hopeful that a repeat is on the cards this summer despite the absence of star openside David Pocock through injury.
Pocock tore his ACL earlier this season and will be sidelined for the entire series but Dwyer believes his unavailability shouldn't have a profound effect on the Qantas Wallabies given their strength in depth at No7 thanks to the presence of Michael Hooper, Liam Gill and George Smith.
"The three of them are world class without any doubt," added Dwyer.
"Pocock was not an especially good attacking player - most Australians got a shock if he ever passed the ball. I wouldn't think any of those players are a step down from him at all.
"Hooper is probably the best attacking player of the lot and, allied to that, he currently has the best work-rate of any Australia No7 by some distance.
"Smith is probably the most physical and the hardest to move over the top of the ball and is certainly the most experienced by a long way.
"He is probably the best guy under pressure; he just doesn't seem to get ruffled at all.
"One of the very well-respected newspaper columnists over here has suggested - if all things are equal - to start with Smith and bring Hooper into the pitch later. That's a possibility."
Dwyer believes the back row will be a key battleground on June 22, June 29 and July 6, with the Lions having picked a glut of talent in that area last Tuesday.
Tom Croft, Toby Faletau, Jamie Heaslip, Dan Lydiate, Sean O'Brien, Justin Tipuric and Sam Warburton provide Warren Gatland will plenty of options but Dwyer isn't convinced that the Australians share a similar spread of quality in all three back row positions.
Dywer is more than happy with the skills offered by Gill, Hooper and Smith on the openside and is content with what Wyclif Palu and Ben Mowen can offer from No8 but he isn't so taken by what's available when it comes to the blindside berth.
"I would like to see a No8 and a blindside flanker in really good form because the Lions selection in those positions will not be easy with so many good players.
"If Wycliff Palu can get back to tip-top form that would be useful because he is such a big bruising guy who can wear down opposition defences.
"Ben Mowen really keeps things under control and his discussions with the referee when playing for the Brumbies have been really good. He can add that maturity.
"We have a few number sixes but none of them stand out as world class.
"I wouldn't like to see some of our first-choice players get injured either - if we lose James O'Connor we lose a bit of sheer brilliance and if Digby Ioane is not up to his best we lose a little of our attacking edge."