Rob and Fern Messenger, who were sacked by the senator in 2017, have claimed the adverse action was taken against them after they escalated workplace complaints to Prime Minister Malcolm Turnbull in that year.

Senator Lambie has claimed she was not aware of the public disclosure document sent to Mr Turnbull when she sent a show-cause letter to the couple on their ongoing employment.

She said she only became aware of the document in a response to that letter from Mr Messenger.

Justice John Snaden on numerous occasions during Tueday's hearing stopped questioning of Senator Lambie by the pair on her alcohol use and workplace talk about her sex life which they say made themselves and others feel uncomfortable.

"If you want to embarrass the senator, do it in another forum," he said.

"What we're doing here is investigating complaints you made and conduct in which the senator later engaged and whether there is a connection between the two."

Mr Messenger argued he was attempting to focus on the complaints, to which Justice Snaden responded:

"It doesn't seem to me that is what you are trying to do.

"It seems to me that you are trying to do something else and I will not permit you to do it."

Cross-examination of Senator Lambie will continue on Wednesday.

The case is expected to end next week.