New South Wales Waratah Wilson, the son of former World Cup-winning Wallaby David Wilson, joins fellow scrumhalves Ryan Lonergan and Tate McDermott in the 33-man squad.
Loosehead prop Lambert earns his spot after a strong season for the Waratahs.
Flyhalf Carter Gordon is recalled while still recovering from a broken leg against Argentina.
Overseas-based forwards, prop Taniela Tupou and loose forward Tom Hooper, have also been recalled, along with Miles Amatosero.
Nick Champion de Crespigny, Toby Macpherson, Zane Nonggor, Aidan Ross, Harry McLaughlin-Phillips, Jordan Petaia and Kalani Thomas dropped from the squad that lost back-to-back tests to New Zealand.
Overseas-based lock Will Skelton, loose forward Charlie Cale and Jake Gordon are among those unavailable due to injury.
Australia lost two out of three Nations Championship tests on home soil in July, falling to France and Ireland.
They will meet England at Twickenham on November 8 before playing Scotland and Wales.
Nations Championship 2026
The inaugural Nations Championship will see six northern hemisphere and six southern hemisphere nations battle it out across six rounds in the July and November international windows before assembling in Twickenham for one unforgettable finals weekend on November 27-29.
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Wallabies Nations Championship Squad:
Forwards: Allan Alaalatoa, Miles Amatosero, Angus Bell, Josh Canham, Massimo De Lutiis, Tom Hooper, Isaac Kailea, Tom Lambert, Fraser McReight, Josh Nasser, Brandon Paenga-Amosa, Billy Pollard, Lukhan Salakaia-Loto, Lachlan Shaw, Carlo Tizzano, Taniela Tupou, Rob Valetini, Jeremy Williams, Harry Wilson (captain)
Backs: Filipo Daugunu, Ben Donaldson, Carter Gordon, Isaac Henry, Len Ikitau, Max Jorgensen, Ryan Lonergan, Tate McDermott, Declan Meredith, Hunter Paisami, Harry Potter, Joseph-Aukuso Suaalii, Teddy Wilson, Tom Wright