Martin has missed the past two weeks due to a hamstring injury sustained against the Eagles in Round 16, while Lynch was ruled out of last Saturday's matchup with North Melbourne with a similar issue.
On Monday the club confirmed neither player will be ready for Round 19, adding further headaches to Damien Hardwick's planning as the Tigers look to return to winning ways.
Young Richmond defender Josh Gibcus was subbed out of the Round 18 loss to the Roos with a shoulder issue, with the teenager still in the frame to feature against the Dockers.
Trio Ivan Soldo (thumb), Sydney Stack (fractured cheekbone) and Jack Ross (knee) all missed the recent defeat and are expected to be available for this weekend's action.
Veteran midfielder Kane Lambert remains in recovery and nursing an Achilles injury, while uncapped ruckman Mate Colina is currently placed in AFL health and safety protocols and is listed as questionable for this weekend.