Flanker Valetini, who missed the first test with a calf injury, was outstanding as Australia took an early 23-5 lead in last week's second test but is being "managed" ahead of two matches against the Springboks in South Africa.
"He's not right this week," coach Joe Schmidt told a press conference on Thursday. "(The calf) just tightened up so ... it's probably precautionary not playing him this week."
Valetini will be replaced in the back row by Tom Hooper, one of four changes to the starting line-up from the second test.
Tighthead Allan Alaalatoa suffered a shoulder injury last week that could rob the Wallabies of one of their leaders for the rest of the season.
Taniela "Tongan Thor" Tupou brings his considerable bulk into the front row in Alaalatoa's place for his first appearance of the series.
"We saw him in the First Nations-Pasifika game and I thought he really worked hard there," said Schmidt.
"So we're hopeful that Taniela can continue that upswing and bring us a real burst of energy."
Dylan Pietsch will start on the left wing for Harry Potter, who was taken off with a hamstring injury after 20 minutes last week.
White's inclusion at scrumhalf for Jake Gordon was not enforced but gives the 35-year-old a chance to win a 73rd cap before standing down from test rugby, a decision he announced earlier on Thursday.
"Whitey's got such massive respect inside the squad that it seemed a fitting way for him to finish," said Schmidt.
"And I'm not a sentimentalist, it's a test match, and you pick people who are capable of playing that test match, and we believe that Nick is."
Schmidt has reverted to a 5-3 split in favour of the forwards on the bench, bringing outside back Andrew Kellaway back into the matchday squad for flanker Carlo Tizzano.
Tizzano was the recipient of the clear-out from Lions counterpart Jac Morgan, which Schmidt felt was illegal, in the lead-up to the tourists' late match-winning try in Melbourne.
"I think it's better that he sits this one out," said Schmidt. "He was still pretty sore but it wasn't a concussion, no."
Schmidt said the squad had been devastated by last week's loss.
"An incredibly deflated group," he said. "Tuesday was tough to get them up off the canvas, and today, there was a little bit of an upswing, and we've just got to keep that momentum."
Wallabies XV v British & Irish Lions:
15. Tom Wright, 14. Max Jorgensen, 13. Joseph Suaalii, 12. Len Ikitau, 11. Dylan Pietsch, 10. Tom Lynagh, 9. Nic White
8. Harry Wilson, 7. Fraser McReight, 6. Tom Hooper, 5. Will Skelton, 4. Nick Frost, 3. Taniela Tupou, 2. David Porecki, 1. James Slipper
Replacements: 16. Billy Pollard, 17. Angus Bell, 18. Zane Nonggorr, 19. Jeremy Williams, 20. Langi Gleeson, 21. Tate McDermott, 22. Ben Donaldson, 23. Andrew Kellaway