Both had been listed as "doubtful" tourists because of injury shortly before Jones flew to France on Sunday to check out training camps for the 2007 World Cup.
But since then Tune, who has been recovering from knee and shoulder surgery, and Lyons (groin and hernia operations) have indicated they will be fit if chosen for the Tests against France, Wales, England and Ireland in November.
Tune believes his recovery is progressing so well that he could be ready for the Queensland Reds' four-match tour of Argentina next month.
"I'd be keen to do both tours," he told The Australian newspaper.
"Even if I play for Australia A (against the French Barbarians in Bordeaux on November 1) it would be great to get the feel of international rugby again."
Lyons needs to show the selectors he can return to the number eight spot quickly after regular flanker Georghe Smith performed admirably in the Wallabies' loss to the All Blacks in Auckland - their fifth successive Test defeat.
"That's the sort of competition we need," Lyons said.
"It's good for the team and I'm sure it will be good for both of us."