"And just like in 1913, economic austerity today is hitting working people hardest," he said.
The 64-year-old actor, who plays the Rob Charles role in Fair City, was 29 when he landed the prized role of Fitz in the Strumpet City television series in 1979.
"Getting the chance to act alongside Peter O'Toole, Peter Ustinov, Cyril Cusack and Donal McCann in Strumpet City felt to me like winning the Lotto," he told The Herald.
Murray is involved in some of the forthcoming events to commemorate the centenary of the Lockout.
He believes it is important to acknowledge the sacrifice, loyalty and endurance shown by significant numbers of people who suffered in the epic 1913 industrial dispute.
The dispute focused international attention on the poor working conditions of many Dubliners who lived in the worst slums in Europe.
The principled struggle by the impoverished workers, which he portrayed as Fitz in Strumpet City, should be honoured. Fitz ended up joining the British army and being sent to the battlefields of the First World War.
So many of those men involved in the Lockout ended up being forced by poverty to go off to the battlefields like The Somme. After everything that happened in the Lockout, the army offered pay and pensions for the families of soldiers.
"I think Dublin, along with London and Manchester, sent the most men to the battlefields. And I think half of them may not have come back," he said.
In honouring those involved in the 1913 struggle, he believed the commemorations also honour all those who lived in the city's tenements.
"I discovered later that my own mother lived in a tenement in Henrietta Street between 1936 and 1940," he said.
"My mother's name was Rosaleen Mary Josephine Patricia Connolly," he said. He later presented a series on tenement life for TV3.
"When James Plunkett Kelly wrote Strumpet City in 1969, the tenements of Dublin were still standing.
"It wasn't until the mid-70s that they were got rid of which was more than 50 years after the founding of the new State," he said.
He said there were a few similarities between the plight of impoverished workers in 1913 and the predicament of stressed out families with heavy debts in 2013.
"It's the working people who suffer in an economic crisis.
"In times of austerity, the main brunt is taken by working people," he said
* Bryan Murray and actress Angela Harding, who appeared with him in Strumpet City, will read from Plunkett's work at the official State commemoration of the centenary on Saturday in O'Connell Street in Dublin.
President Michael D Higgins will attend the event. The two-hour State commemoration, beginning at 12.30pm, will include a dramatic re-enactment of the infamous baton charge.