Lutsenko has accused Pshonka and his subordinates of violating his human rights and parliamentary immunity, and of arbitrary arrest and unlawful imprisonment.
Lutsenko is in prison in Ukraine, accused of abuse of power while in office.
A verdict is expected in that case on February 27.
The suit was registered in court in the District of Columbia in December.
The plaintiff was instructed by the court to serve the defendant and file a status report with the court on February 8. When no report was filed or extension sought on February 8, the court extended the term until February 24.
As no status report was filed or cause shown why the action should not be dismissed, the court threw out the suit.