Lambert suffered hip soreness in the second half of the Dreamtime contest, substituted out late in the third quarter. The 30-year-old was playing just his fourth game back after an ongoing hip concern hampered the start of his season.
Lynch spent the fourth quarter of the match on the bench with a hamstring concern, the second time this year the current Coleman leader has had trouble with the tendon.
Hardwick gave an update on the two after Richmond's win, praising Lambert's courage for managing his ongoing hip issue.
"Those boys won't play next week. We'll assess the damage and go from there," Hardwick told media on Saturday night.
"It is concerning. Any other player wouldn’t be playing, to be perfectly honest. What he (Lambert) does to get up for games is incredible.
"We thought we would get one – at a maximum two games – he's played the last four. Probably shows you how important he is that we start winning our games.
"His leadership both on and off the field is really important. He does effectively get a two-week break as well with the bye coming up. He is tough this guy, really, really tough. The game means a lot to him in fairness, so that’s why he keeps pushing through."
"He was touch and go. We thought he was no chance. He pushed and wanted to play such a significant game and then captain's run he just decided he wasn’t quite right," Hardwick said.
"We had fit players. Jack Ross came in and did a really good job, but Jack will be available to play next week at this stage."