Martin's behaviour has been the subject of rumour in the pre-season, stories that were dismissed by both the club and coach Damien Hardwick.
Speaking on AFL.com.au's panel show Footy Focus, Lyon says the situation remains a concern for the Tigers.
"Make no mistake, there are some issues with Dustin at Richmond," Lyon said.
"People can deny all they want, but his off-field stuff remains an issue for the Richmond Football Club."
Lyon said it was a shame to see such a prodigious talent struggle with the demands of AFL football.
"We know what he's capable of," he said.
"We know that he's a young man that's only been in the system a few years and doing stuff that the Judds, if you like, do on a regular basis.
"The on-field he can do. It's the off-field that he needs to get sorted out.
"Don't be under any illusion that the Richmond footy club aren't aware of it, and aren't dealing with it and are putting some pressure on him."
Should that not work, Lyon conceded that trading Martin could be a possibility.
Lyon also cast an eye over the rest of the competition, claiming this season was 'make or break' for the likes of North Melbourne's Lachie Hansen, Western Bulldogs midfielder Shaun Higgins and Hawthorn's Ryan Schoenmakers.
