The alleged incident is the subject of an investigation by Sharks management, with the NRL asserting they would take a zero tolerance approach towards abuse of referees by first grade players.
The Fifita twins and Lodge have five days to decide if they will appeal the ban.
The Sydney Morning Herald reported on Monday, David Fifita was banned for 12 months over a similar incident in 2011, while according to News Corp the brothers were involved in another incident in 2013.
According to a copy of Hannon's report of the incident, obtained by the Herald, David Fifita said to the referee: "You're a f***ing disgrace mate. I lost respect for you when you didn't stop time when one of our players were down. You're a f***ing disgrace".
David Fifita then allegedly continued to abuse Hannon for 20 seconds before his brother joined in.
"(Andrew) charged towards me and attempted to snatch my mobile phone which I was holding in my right hand," the report continued to read.
"Numerous people intervened and held Andrew Fifita back preventing him from grabbing my mobile phone. At the time these actions by Andrew Fifita made me feel very threatened and uncomfortable."
Lodge, who played in the Tigers' NYC loss to Sydney Roosters on Friday night, is no stranger to drama either. He was suspended last season after writing the word c*** on his wrist strapping while playing for NSW's Under-20s side.
Former leading referee Bill Harrigan has called for the Fifita brothers to be banned for a year from the NRL, if the allegations are proven.
Harrigan, who refereed 10 grand finals, 21 State of Origin fixtures and 22 Test matches, said the Fifita brothers needed to be made an example of, if they were found guilty.
"It should be a long time out of the game," Harrigan told Triple M radio.
"Because that's what they are saying about anyone out there approaching referees, and trying to retain young referees over the abuse they all cop.
"To cop it from a first grader to say 'I'll smash you' or something similar if that is what he has said. To me it has to be rubbed out to set an example, rubbed out for 12 months.
-AAP