(CNN) A federal judge hearing arguments in a potentially critical impeachment inquiry case wants to hear from lawyers for the Trump White House, the House of Representatives and from impeachment witness Charles Kupperman on Thursday after Kupperman filed a lawsuit asking the federal court to decide whether he would need to testify.

Kupperman's House testimony had been set for Monday, but Kupperman didn't show up, citing White House and Justice Department reasoning that he was immune from testifying because of his previous work on the National Security Council.

Leon will meet the parties in court at 3 p.m. on Thursday, "due to the time-sensitive nature of the issues raised in this case," Judge Richard Leon of the DC District Court wrote Monday night.

Kupperman, who served until last month as deputy national security adviser at the White House, was listening in on the July 25 phone call when, according to a White House transcript, Trump pressed Ukrainian President Volodymyr Zelensky to investigate former Vice President Joe Biden.

Kupperman's lawsuit raises additional questions about possible testimony from former national security adviser John Bolton, as Kupperman's lawyer Charles Cooper also represents Bolton.

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