Lolesio was stretchered from the field after appearing to suffer whiplash in an ugly second-half collision in the Wallabies' 21-18 win over Fiji in Newcastle on Sunday.
While the ACT Brumbies ace was initially cleared of a serious neck injury, he was readmitted to hospital on Tuesday for follow-up surgery.
The Wallabies didn't reveal any further details of his injury and said the 25-year-old would "spend a period of time away from the game" and was expected to make a full recovery.
Lolesio's injury means he may have played his last Test for Australia, having signed to play in Japan.
The Wallabies will name their squad for the three-Test Lions series on Friday, with the first match in Brisbane on July 19, with youthful duo Tom Lynagh and Ben Donaldson now expected to tussle to wear the No.10 jersey.
Speaking ahead of the Lions clash with the Brumbies in Canberra on Wednesday night, Lions assistant coach Sexton was asked his thoughts on the Wallabies' flyhalf candidates should Lolesio be ruled out.
Lolesio had started 11 of the 13 Tests under Wallabies coach Joe Schmidt.
"I think Lynagh has been excellent all year. I think Donaldson did really well when he came on. I think they're both quality players," Sexton said.
"But obviously Lolesio's their number one based on their last, whatever, 10 games. He played the majority of the big games under Joe (Schmidt), so he'll know Joe's way. So he'll be a loss for them."
The former Lions No.10 refused to bite when asked if he was surprised Schmidt opted not to select veteran playmaker James O'Connor.
"I'm not going to question Joe Schmidt's selection, which is probably what you're hoping for, and create a headline," he said.
"But no, outstanding three guys that are in there. They're probably guys that know Joe's system, Joe's way of playing, and they're the three that Joe has gone with and the three we're preparing to play against."
Despite hopes of a fairytale international farewell, O'Connor also missed out on a berth with the AUNZ Invitational squad to take on the Lions this Saturday.
The visitors have not shied away from recalling a veteran fly-half of their own in Owen Farrell.
In a bold move, Lions coach Andy Farrell drafted his 33-year-old son into the squad mid-way through the tour after Elliot Daly broke his arm against the Queensland Reds.
Though Farrell hasn't played in 10 weeks since suffering a concussion with French side Racing 92, and has not been used by England in almost two years, Sexton backed him to make an immediate impact in his fourth Lions tour.
"As you'd expect with someone with that experience, he's fitted in. He must have had the playbook on the plane on the way over because he came in and he's not missed a beat," Sexton said.
"He's been on top of things in training and that's exactly why he (Andy Farrell) picked someone with experience and knows about a Lions tour, because it might take someone else 10 days to fit in. He's hit the ground running."
Farrell was not named in the Lions squad to face the Brumbies on Wednesday but his father confirmed he was in contention for the AUNZ XV clash on Saturday.
