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Gatland, who oversaw the 2-1 series victory over Australia four years ago, is tipped to select Welsh flanker Sam Warburton as captain for the second time, an honour previously bestowed only on England's Martin Johnson.
Warburton captained the team in the first two tests against Australia in 2013 but missed the decisive third through injury, with fellow Welshman Alun Wyn Jones stepping in.
Jones has taken on the captaincy duties for Wales this season while Warburton has played superbly, adding to the conundrum for Gatland, who will return to his day job as Wales coach after the tour.
There will no doubt be the usual surprises - experienced Six Nations men missing out and the odd young "bolter" being given their chance. Media speculation over the weekend has already suggested that Joe Launchbury, George Ford and Jamie Joseph can start preparing for England's tour of Argentina instead.
The heart of the squad oozes quality, with first five-eighths Jonathan Sexton and Owen Farrell, halfback Conor Murray, winger George North and key forwards Billy Vunipola, Peter O'Mahony, Taulupe Faletau and Sean O'Brien on just about every pundit's short list.
Gatland also looks spoiled for choice at lock and in the loose forwards, where some high-class operators will have to miss out.
On the other hand, other areas will have given him sleepless nights, with a group of similarly matched contenders of a good standard but who are unlikely to strike fear into New Zealand coach Steve Hansen.
Key among those is probably hooker, where the captains of the best two teams in Europe - England's Dylan Hartley and Ireland's Rory Best - will probably travel but with neither in the box seat - and Wales' impressive Ken Owens in with a shout.
For all those who make the squad, and however well they bed down in their short time together, they face a monumentally difficult task.
Many observers are describing this year's tour as the Lions' toughest, not just because of the supreme quality of the world champion All Blacks, but because of the strength too of the provincial teams and the desperately limited preparation time.
The Lions kick off with the only easy-looking fixture of the 10-match tour, against Provincial Barbarians on June 3.
That is just one week after the English Premiership and Pro-12 finals, and with Gatland having said previously that anyone featuring in those matches will not play in the tour opener, his opening options look squeezed.
Former England first five-eighth Stuart Barnes, who toured New Zealand with the Lions in 1993 without playing a test, described this year's tour as "attempting to conquer rugby's Mount Everest without oxygen, with a storm gathering on the horizon.
"To win the series would be the greatest Lions triumph of all. To win more than 50% of their games will be a decent effort," he said, factoring in the tough tour games against the country's dominant Super Rugby sides.
The Lions have won only one series in New Zealand, in 1971, and since they started touring there in 1904 have won six of the 38 tests - with three draws.
They were hammered 3-0 on their last visit 12 years ago, when Dan Carter was in his pomp, but if Lions fans think the retirement of the superstar first five-eighth will have weakened the All Blacks, they have not been watching Beauden Barrett, who is operating at arguably even higher levels this season.
His, and possibly New Zealand's only relative weakness is in goalkicking, where the Lions have real strength in depth, but the tourists are almost certainly going to need to find more than a few penalties to conquer that sporting Everest.