They've also laboured through a breakneck schedule on Kiwi soil, with nine matches in just 35 days - and another to come.
Since arriving down south, Lions players have been seen jetboating, strolling around town and visiting sites like Milford Sound and The Fear Factory.
The All Blacks, meanwhile, have been in their usual central Auckland confines, dissecting what went wrong in Wellington.
"Hey, if that's what they think will get the best out of their players, good on them - for us, we've got a lot of improvements to make," flanker Kaino said.
"I think we'll just worry about what we need to do.
"We have little pockets where guys have that balance, can enjoy being in the (All Blacks) environment - but not too relaxed."
The contrast is even more pronounced given what lies in store, with the Lions chasing a first series win in New Zealand since 1971 and the All Blacks hellbent on defending their 23-year Eden Park unbeaten run.
The 34-year-old Kaino, who played in both the 2011 and 2015 Rugby World Cup finals, said Saturday's third-Test decider was of a similar magnitude.
There was plenty of energy at Tuesday's training session, with players doing all they could to earn a starting berth for the match.
"Being one-all, it does have that feel about it," Kaino said.
"I'm getting excited about the prospect."