The 18-year-old made a big impression at the Swans in his first pre-season, leading to a debut in Round 1, where he collected eight disposals.
Sheldrick was dropped to medi-sub in Round 2 before returning to the VFL for the Swans' reserve side. In what is a cruel blow for the young midfielder, Sheldrick appears set to miss a large chunk of the season.
"Angus Sheldrick had an operation on the cartilage, so he had a bit of work done on his knee," Longmire told media.
"So he's going to be out for a couple of months."
Ruckman Tom Hickey is recovering well from a knee injury suffered in Round 3 and will push for selection in coming weeks.
Hickey made a shock return from a knee injury last season, missing just the one game after initially being ruled out for six to eight weeks.
Originally forecasted to be out for at least six weeks after his latest setback, Longmire said the 31-year-old is ahead of schedule in his return and is looking good in training after just four weeks on the sideline.
Despite this, Longmire reassured that the club will be cautious in his recovery before giving him a potenitally early return to the 22.
"He's coming along really well, he's remarkable," Longmire said of Hickey.
"He trained today and looked good. We're not sure what the rest of the week looks like for him.
"He probably is [ahead of schedule]. We won't play him unless he's ready to play, we're mindful of that. We're not gonna put him out there if he's not ready to go.
"But at the moment he looks like he's coming along pretty well. He's really positive the way he takes his rehab and his injuries... he's just got a positive attitude, which I think really helps."
The Swans will be without key-position duo Logan McDonald and Paddy McCartin for their clash against the Lions on Sunday, with Longmire confirming that both have entered the AFL's concussion protocols.
"They're fine, they're both really good," Longmire said.
"They obviously go into the concussion protocols. So they won't play this week."
Longmire said Papley's return will be subject to passing some final checkpoints in training this week before the Swans confirming his return.
"Over the last week he's been absolutely flat out," the Swans coach stated.
"Trained again today, look really sharp. If he gets through the rest of the week training, which we expect he will, he'll be selected in the squad."
Longmire confirmed that Robbie Fox was still a couple of weeks away as he works back from a hamstring injury, while Irishman Colin O'Riordan is back in training after suffering an eye injury early in the season.