In the same fixture last year, with Lam also at the helm, the Barbarians stunned England 63-45. With a squad like this they have a strong chance of pulling off another upset.
After a heavily injury-disrupted season, Piutau made a try-scoring return for the Bristol Bears against Sale Sharks this month and will be keen to replicate his debut for the Barbarians against Fiji six years ago in which he scored a try.
Aside from the Kiwis, Mata could do some serious damage.
An Olympic sevens gold medallist with Fiji, Mata was named the Pro-14 Players' Player of the Year this month after helping Edinburgh to the knockout stages of the European Champions Cup.
Mata was also part of the Fiji side that stunned France for the first time in November last year, and he promises to be a force at the World Cup in Japan.
Welsh halfback Rhys Webb and Fijian wing Filipo Nakosi are other already-announced squad members.
Lam hopes the Baabaas will produce a performance to honour the memory of long-standing club president Micky Steeele-Bodger, who passed away aged 93 last week.
"Everyone involved in rugby was sad to hear about Micky's passing," Lam said. "He was such a great character, gave so much to the game for so long, and held strong beliefs about the way it should be played on and off the field.
"The players and management will honour his memory as much as we can in the competitive and exciting way we try to play the game, and in the friendships that will be established by a unique group of players."
