Tarrant will be a notable absentee from the team sheet for Richmond's final pre-season hitout, with the club saying the 33-year-old is "managing some hip symptoms and is unavailable in the short term".
With Richmond's season opener against Carlton just 15 days away, Tarrant has little time to prove his fitness.
The news is better for Lynch, who has recovered from his foot injury and will take on the Demons.
"Presuming Tom completes training on Thursday, he will be available for reduced game time on Saturday against Melbourne," Richmond's medical report said.
Liam Baker (appendix removed) and Nathan Broad (hamstring) are also on track for some game time.
Geelong will be lacking some premiership starpower for Thursday's practice match against Brisbane, with Jeremy Cameron, Isaac Smith and Mitch Duncan (calf) all unavailable, along with new recruit Jack Bowes.
They join forward Tom Hawkins (foot) and defender Jack Henry (foot) as key absentees, but Gary Rohan has been named to return.
"Jeremy and Isaac haven't missed a beat through pre-season and are in a good position," Geelong football manager Simon Lloyd told the club's website.
"We have got what we need through a large number of training sessions and last week's match simulation against Hawthorn."
Brisbane will be without former skipper Dayne Zorko (hamstring).
Port Adelaide have lost recruit Junior Rioli (illness) and Travis Boak (ribs) for Thursday's clash with Fremantle, but Charlie Dixon, Zak Butters and Darcy Byrne-Jones all return.
The Dockers will be without big man Luke Jackson (concussion) and are still missing Michael Walters, Luke Ryan and Michael Frederick, but Heath Chapman returns.
Collingwood have named new recruits Billy Frampton, Bobby Hill, Dan McStay, Tom Mitchell and Oleg Markov for their match against Hawthorn on Thursday.
Brayden Maynard is out after an abrasion he suffered last week became infected.
The Hawks welcome back veteran forward Luke Breust and defender Changkuoth Jiath.
Draftees Cam Mackenzie and Henry Hustwaite have also been named.
