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.
Henchman Robert Jennings, who set the 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 Scott Court blaze.
Snowden has laun-ched an appeal against his conviction, while Jennings is appealing against both his conviction and sentence.
A procedural hearing on the appeals will take place on April 30 at the High Court in Edinburgh.