Arthur Hutchinson claims that the jail term amounts to inhuman and degrading treatment as he has no hope of release.
The killer, now aged 75, broke into a home in Dore before stabbing to death Basil and Avril Laitner and then knifing their son Richard. Just hours earlier on that fateful night in October 1983 the family had hosted a wedding celebration.
It was thought that Hutchinson's motive was to commit armed robbery. The Hartlepool-born killer went on the run but was later caught. He accused a newspaper journalist of committing his terrible crimes but was found guilty and jailed for life in 1984.
In 2015 a judgment from the European Court of Human Rights found there had been no violation of Article 3 of the European Convention on Human Rights.
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But Hutchinson applied for the case to be passed to the Strasbourg court's Grand Chamber, which will deliver its findings this afternoon.
The judgment will bring fresh scrutiny of the protracted issue of "life means life" terms.
The judge in his original trial ruled that he should serve a minimum of 18 years but then-home secretary Leon Brittan later determined he should face the whole-life tariff.
In 2008, Hutchinson had a domestic appeal against whole-life tariffs kicked out by the Court of Appeal.