Anselm Ribera and Christopher Morrissey from Birmingham, and Declan Morrissey from Solihull, were found guilty of the murder of Craig Hodson-Walker and the attempted murder of his father Ken, during the raid at Fairfield Post Office and Village Store in January last year.
The trio were also found guilty of possession of a firearm with attempt to endanger life and attempted robbery. They will each serve a minimum of 34 years in prison.
Justice Colman Treacy, who presided over the case, said that their prospects of release at any point in the future were "slim".
He also branded them "parasitic criminals" and "a real danger to the public".
Craig's mother Judith said: "The punishment of these mindless dregs who murdered Craig will never equal the pain they have caused us."
She added that the family had been heartened by "fantastic support from the community".