The Dons are believed to have offered around £100,000 for the teenage midfielder they signed under freedom of contract last month.
However the Lanarkshire club insist that comes nowhere near the fee they want for someone who made 14 top-team appearances for the club last season.
Instead they want up to nine times that amount which is why the Aberdeen manager is ready to take his chances with the tribunal rather than continue talks.
McInnes said: “We’ll go to the tribunal but I’m confident and comfortable that we’ve done our due diligence and the tribunal outcome will reflect that. But Hamilton have got such a high regard for Lewis so I’m not surprised it’s going to a tribunal.”