Scott Snowden, 39, and Robert Jennings, 51, were found guilty of killing three members of the Sharkey family in July last year.
Snowden was ordered to serve at least 33 years in prison for ordering the fire.
His henchman, Robert Jennings, 50, who set the lethal blaze, was sentenced to a minimum of 29 years.
Thomas Sharkey, 21, and his eight-year-old sister Bridget died in a blaze, which started while they slept at their home in Helensburgh on July 24 2011.
Their father, Thomas Sharkey Snr, 55, died in hospital six days later, while mother Angela, 48, survived the at Scott Court blaze.
The court heard how on the morning of the fire Jennings poured petrol through the Sharkey's letter box on the instructions of Snowden, who was in Mexico at the time.
Snowden has launched an appeal against his conviction, while Jennings is appealing against both his conviction and sentence.
A spokeswoman for the Scottish Judiciary confirmed a procedural hearing on Snowden and Jennings' appeals would take place on April 30.
It will take place at the High Court in Edinburgh.
The pair were convicted of the three murders and attempting to murder Mrs Sharkey in July.
Following the verdict, Mrs Sharkey said "justice had been done".