Choje Akong Tulku Rinpoche was stabbed to death in the Chinese city of Chengdu last October.
The 73-year-old co-founder of the Kagyu Samye Ling Monastery in Eskdalemuir, in the Scottish Borders, was said by police to have been killed in a financial dispute, along with his nephew Loga and assistant Lama Chime Wangyal.
A spokesman for the monastery said that Tudeng Gusha (also known as Thubten Kunsal) and Ciren Banyue, his nephew, were being tried for intentional homicide, while Tudeng's other nephew, Geni Jiangcuo, was on trial for harbouring a criminal.
Reports from China said that Chengdu's Intermediate People's Court was told that Tudeng had come to Akong Rinpoche's house demanding 2.7 million yuan (£270,000).
Tudeng, a sculptor, was demanding payment for a number of statues he had carved during a five-year stay in Scotland and London.
The Buddhist teacher declined to give him the money he was seeking, and after four more fruitless visits, Tudeng brought his nephew Ciren Banyue with him and they stabbed the three victims to death, the court reportedly heard.
A spokesman for the monastery said before the hearing: "We understand that Tudeng Gusha claimed that he was owed money for sculpting work which he had previously done at Kagyu Samye Ling, Scotland and Kagyu Samye Dzong London and that immediately before the murder he demanded money from Akong Rinpoche.
"We have provided the Public Security Bureau with documentary evidence and also witness statements to prove that when Tudeng Gusha was working at Kagyu Samye Ling Scotland and Kagyu Samye Dzong London it was agreed that he would not be paid a salary but that all his expenses would be paid and that no money was owing."
A spokeswoman for lawyers representing the families of the three victims said: "The trial started yesterday and ended this afternoon. The judgement will be pronounced later, on a date to be fixed."