The case was launched after Mr Murdoch decided to change the trust over concerns about a “lack of consensus” among children, the Times reported.
Lachan is believed to be more conservative than his siblings and will maintain the legacy of his media brands.
Since the 1960s, Mr Murdoch has built a global media giant with great political and public influence.
Its two companies are News Corporation, which owns newspapers including the Times and Sun in the UK and the Wall Street Journal in the US, and Fox, which broadcasts Fox News.
Mr Murdoch groomed his two sons to follow in his footsteps from the time they were teenagers, journalist Andrew Neil told the BBC’s 2020 documentary The Rise of the Murdoch Dynasty.
“Family has always been very important to Rupert Murdoch, especially in terms of building a dynasty,” said the former Sunday Times editor.
In 1999, the Murdoch family foundation, which owns media companies, had to deal mainly with succession issues.
This led to Mr Murdoch giving his eldest children various jobs in his companies.
The trust gives the family eight votes, which it can use to vote on the boards of directors of News Corp and Fox News.
Mr Murdoch currently controls four of those votes, with his eldest children in charge of one each.
The trust agreement said that on Mr Murdoch’s death, his votes would be transferred equally to his four eldest children.
However, differences in opinions and political views led to discord in the family.
The fight to change the trust was not about money, but about power and control over the future of the Murdoch empire.
The commissioner’s ruling is not final, the Times reported. The court filing acts as a recommended resolution, but the district judge will still make a decision and may make a different decision.
Additional reporting by Michelle Fleury and Charlotte Edwards
