The three-Test tour is the first time a tier-two rugby league nation has embarked on such a venture in England.
Woolf, also assistant to Wayne Bennett at NRL side the Dolphins, coached St Helens to three consecutive Super League grand final wins from 2020-22 and to the 2021 Challenge Cup title.
Since taking over Tonga's national side in 2014, Woolf has overseen a great leap forward.
In 2017, Tonga reached the World Cup semi-finals for the first time, toppling New Zealand in Hamilton along the way.
Two years later, Woolf helmed the Pacific islanders to famous victories over Australia and Great Britain.
Sunday's clash against the Lions at Totally Wicked Stadium signals the culmination of a decade of toil.
"Historic is a great word for it and it is a special occasion for us," Woolf told AAP.
"We know the enormity of being the first team outside of Australia and New Zealand to be invited to do such a tour.
"That shows how far this group has come and is a showcase of Tonga's international standing.
"We are very proud to be in that position and we want to make sure we make the most of it."
Last year's World Cup quarter-final loss to eventual finalists Samoa was a blow, but the hurt from that defeat reveals how far the side has come.
"We were disappointed. We underachieved at the World Cup where we thought we had a side that could give it a real shake," Woolf said.
"This tour gives us a chance to redeem ourselves. We know if we are going to have success at the next World Cup (in 2026) we need to perform at our best a long way from home.
"We have picked old statesmen who know what it takes to win and we have picked for the future with a group of talented young guys that have made their mark in the NRL."
Gold Coast prop Moeaki Fotuaika, Manly second-rower Haumole Olakau'atu and South Sydney forward Keaon Koloamatangi will still be in their prime at the next World Cup, while outside backs such as Parramatta's Will Penisini, St George Illawarra's Moses Suli and Sea Eagles speedster Tolutau Koula are also key to future success.
Veteran Newcastle forward Tyson Frizell, who won the 2017 World Cup with Australia, is part of the touring party and is set to represent Tonga for the first time.
