A hearing took place yesterday at Nenagh Circuit Court regarding the summonses which allege that the Independent TD Mr Lowry, aged 60, of Glenreigh, Holycross, Co Tipperary, knowingly filed incorrect tax returns on October 31 of 2003 and on August 3, 2007.
Mr Lowry was sent forward for trial from the district court to the circuit court earlier this year.
At Nenagh, Patrick Treacy, for Mr Lowry, said he was asking the court to strike out the proceedings against his client.
Judge Thomas Teehan heard legal debate on the case from Remy Farrell, prosecuting, and Mr Treacy throughout the day.
The legal debate will continue on November 10.
Mr Lowry arrived at the courthouse in Nenagh at about 10.15am yesterday. After entering the building alone, he consulted with his legal team before the hearing began before Judge Teehan.
The judge is also due to give a ruling on an application made by the prosecution in July to have the case moved from Tipperary to Dublin.