Senator Lambie is a swing vote in the Senate, giving her the balance of power and therefore significant influence over the fortunes of government legislation.

The senator has so far used her sway to broker a deal with the Morrison government to have Tasmania's $157 million public housing debt waived in exchange for her support for income tax cuts.

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And she's signalled that she may seek concessions on Tasmania's health system, as well as vocational education in the state as part of future discussions with the government.

Now Senator Lambie is suggesting she could raise the issue of a possible royal commission into veteran suicide rates in Australia.

The senator is herself an army veteran and was embroiled in a highly publicised dispute with the Veterans' Affairs Department, which began when she applied for compensation for depression resulting from a back injury she sustained in the line of duty.

The department refused her application.

Senator Lambie said it was "only going to be a matter of time" before a royal commission into veteran suicide was called.

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"We're heading towards a royal commission whether [the federal government] want to hear that or not," she said.

"We have a major problem here between the Department of Defence, our transition, which is non-existent, and Veterans' Affairs and it won't be long before I start having to stamp my feet on the ground and actually doing a deal if that's what it takes after Christmas, to get a royal commission into what is going on with the Department of Veterans' Affairs.

"I'm absolutely stacked up in my office with those veterans already coming through and also members serving in our defence forces that have been bullied and harassed."

A recent report from the Productivity Commission found that the veteran suicide rate was higher than the suicide rate for the general population and that suicide had caused more deaths for contemporary Australian Defence Force personnel than overseas operational service had.

There were 59 deaths of ADF personnel on deployment between 2001 and 2016, while there were 373 suicides among serving, reserve and ex-serving ADF personnel in the same period.

RSL Tasmania chief executive Noeleen Lincoln said veteran suicide was something that was not "one of those things that's easily identifiable and easily fixed".

She said she preferred not to comment on the push for a royal commission, saying "that would have to be a view that would come from probably the board more so than from me".

A Veterans' Affairs Department spokesperson said the federal government recognised the sacrifices made by ADF personnel.

"Regarding calls for a royal commission, the Prime Minister has made it clear that all options continue to be on the table," the spokesperson said.

"The government is committed to ensuring serving and ex-serving ADF members have access to the right support, when and where they need it and provides more than $11 billion per year in support for veterans and their families."