In 1993, Fitzpatrick led the All Blacks to a 2-1 series victory over the tourists in what was the last Lions tour of the amateur era.
The Lions' previous trip to New Zealand was in 2005, where they lost all three Tests under the guidance of England's 2003 World Cup-winning coach Clive Woodward.
But even against the double defending world champion, Fitzpatrick believes the outcome may be different this time around under Warren Gatland, who announced his 41-man squad on Thursday (AEST).
"Having just come back from New Zealand, I think that they may be underestimating just how strong this squad could be," Fitzgerald told Sky Sports. "I think Warren Gatland has picked a team that can win the New Zealand public over - I think in 2005 they got that totally wrong.
"New Zealanders love the Lions - there is a whole generation who could name the whole 1971 squad, people like me whose hero was Gareth Edwards. Grant Fox started to kick around the corner because Barry John kicked around the corner."
Gatland was also in charge for the Lions tour to Australia in 2013, where he guided the visitor to a 2-1 series victory.
That success was the Lions' first since the tour to South Africa in 1997 and Fitzpatrick is predicting a tight series between the sides.
"All the games in New Zealand are going to be hugely competitive and I think it is an asset to have a former All Black coaching the British and Irish Lions. He knows what is needed to win," Fitzpatrick said.
"I think the Lions will struggle in the first test at Eden Park but there is an opportunity for the Lions in the second Test and they could go into the third test all square which would make it very interesting."
The Lions kick off their tour with a game against the New Zealand Provincial Barbarians in Whangarei on 3 June, the first of six games in preparation for the opening Test on 24 June.