Avatar: The Last Airbender's series finale revealed that many of the old masters and mentors the Gaang met along their journey were in truth part of the same secret faction known as the White Lotus. Iroh, Bumi, Jeong Jeong, Pakku and Piandao were some of the most formidable forces in the world of Avatar, and they united that force to liberate Ba Sing Se and restore balance to the world.
The secret society's full membership was never revealed, and with so little time to delve into the nature of the Order, it's entirely possible that there were other members the Gaang met along the way they had no idea about. Bumi handwaved the story of how all the members of the secret society knew each other with the explanation: "All old people know each other. Don't you know that?" If that's the case, these five characters might be secret members of Avatar's most powerful faction.
The powers of the many characters the Gaang came across on the course of their quest across the globe were not merely limited to the elemental arts of bending. One of the most unique forces that made their acquaintance was Aunt Wu, the fortuneteller of Makapu Village whose abilities were so reliable that the town around her grew to rely on her predictions in the operation of their individual lives. Who could possibly be more valuable to the White Lotus?
Wu certainly had the same air of playing her tarot cards close to the chest when it came to not fully revealing who she was, and at the end of the episode she was primarily featured in she let Aang in on the "secret" that he was capable of shaping his own destiny. That proved to be a crucial plot point for the series. It would only make sense that the White Lotus was guiding Aang in the right direction all along. It would also add more depth to Wu's flirtation with Iroh in "Bato of the Water Tribe," and who wouldn't want more of that?
Every confirmed member of the White Lotus served as masters and mentors to much of the cast: Iroh taught Zuko, Pakku taught Katara and Piandao trained Sokka. Aang had even more masters, with Bumi teaching him a valuable lesson in creative thinking while Jeong Jeong was his very first firebending instructor. One crucial advisor, however, was missing from the series finale: Guru Pathik.
Pathik helped return Appa to the Gaang and guided Aang through opening his chakras in order to master the Avatar State. He is one of the oldest people seen in the series, wielded unique abilities with chi manipulation that allowed him to bond with Appa. His spiritual mastery would be more than welcome among the White Lotus' ranks. It's quite possible Pathik was a pacifist, however, which would go a long way in explaining why he took no part in Ba Sing Se's liberation.
The core beliefs of the White Lotus involved the valuation of beauty and truth above the national borders that locked the world into a state of violent war, and few characters could embody that ethic more than Shyu. Looking to his own family as the source of his beliefs, the Fire Sage defied the Fire Lord's orders to apprehend the Avatar and instead assisted Aang in a time when he needed it most.
Shyu was one of the earliest examples in the series of a Fire Nation citizen acting against the national interest for the greater good. Iroh and Jeong Jeong were among the other early examples of the same belief, and both of them were steadfast members of the Order. Shyu would be a natural fit, and they would welcome him gladly. With his advancement to the position of Great Sage of the High Temple, he would doubtless be an influential figure in the days after the war.
A peculiar character from early on in the series, Oyaji was the village leader to Kyoshi Island. Despite his position of political influence, however, his pride over Kyoshi Island's isolation from the war, his hesitancy to join it and his accusing Team Avatar of being Fire Nation spies don't exactly make him a likely candidate for being a White Lotus member.
However, one of the series' core themes involves how often things change, and it's not like Oyaji would be alone among the Order as a stubborn old man whose views shifted over time. With the Kyoshi Warriors ultimately deciding to travel the world extending their aid to all people, it's clear that Oyaji had a change of heart, and the Order's philosophy would be perfect for him to embrace.
With a mysterious past hinted at in the tinkerer's tales, the Mechanist's liberation from beneath the Fire Nation's thumb and his exhilaration at being able to use his inventions for the good of humanity hint at one of the most potent emotional journeys for a relatively minor side character. The White Lotus say that they revere "philosophy and beauty and truth," all ideals the Mechanist holds in high esteem.
It's highly unlikely the Mechanist was a White Lotus member all along, but given his unbridled passion for exploring truth, he would possibly be one of the most natural fits for joining the Order following the Hundred Year War. It's known that by the era of Korra, the White Lotus came out of hiding, and the inventor whose genius changed the world would likely be ecstatic about joining their ranks.