Mr Lett enlisted in the Australian Imperial Force in January 1916, and left Australia in November aged 39.
Records collected over the years by Mr Foster show en route to Europe aboard the SS Port Napier, Mr Lett was docked a day's pay for gambling.
John (Jack) McLaren Lett.
He was deployed to France where he fought in the Battle of Passchendaele and was killed in the Battle of Polygon Wood on September 27, 1917.
Mr Foster owns a metal hat his grandfather made while in the trenches at Passchendaele, made out of an 18-pounder shell casing. He used buttons, ribbon and insignia from his uniform to adorn the cap.
"Fancy cutting that out while you're in the trenches," Mr Foster said.
A telegram from a man who fought beside Mr Lett said about 6am that day, "we went over" and about an hour later, Mr Lett was hit by a piece of shell and killed instantly. It is believed he was killed by friendly fire.
The telegram said the shell "blew off part of his head" and his body was lying about 150 yards (137m) into no-man's land.
Further telegrams reveal Mr Lett's final resting place was unknown. His name is remembered on the Ypres (Menin Gate) Memorial, together with more than 54,000 officers and men whose graves are not known.
About six weeks ago, Mr Foster travelled to Albany, Australia, for a relative's wedding. While in the city, he visited the National Anzac Centre, but he could not find any details of his grandfather.
A highlight was seeing the place the ships departed for Europe 100 years ago.
Mr Foster said he had always attended civic services through his life and is a member of the Tauranga RSA.
"Anzac Day is important to remember the people who fought in it, especially if they were relatives."
About 20 years ago, Mr Foster began researching his grandfather to find as much information about him as he could. He now boasts three folders of information.
"He was my grandfather and I just wanted to find out as much as I could," he said.
