It is difficult to imagine a stronger assertion of the teaching of the Catholic Church on abortion and euthanasia than that contained in n.83 of Amoris Laetitia. On both points, Pope Francis' words address the subjects in relation to the context of today:
So great is the value of a human life, and so inalienable the right to life of an innocent child growing in the mother's womb, that no alleged right to one's own body can justify a decision to terminate that life, which is an end in itself and which can never be considered the "property" of another human being. The family protects human life in all its stages, including its last. Consequently, "those who work in healthcare facilities are reminded of the moral duty of conscientious objection. Similarly, the Church not only feels the urgency to assert the right to a natural death, without aggressive treatment and euthanasia", but likewise "firmly rejects the death penalty".
For some, it has been the reference to the death penalty that has prompted comment. But I am finding more interesting the language of a "right to natural death". The term is cited in a quotation from the Relatio Finalis of the 2015 Synod, n.64, which, in its turn, includes a reference to the Catechism of he Catholic Church "cf CCC, 2258", the paragraph which opens the Catechism's treatment of the fifth commandment:
God alone is the Lord of life from its beginning to until its end: no one can under any circumstance claim for himself the right directly to destroy an innocent human being.
I am not aware of the term being used previously in the teaching of the Catholic Church (correction, please, via a comment if I have got that wrong), and nor does it occur in the major international human rights instruments (the UN Universal Declaration of Human Rights or the European Convention on Human Rights).
The paragraphs of the Catechism which immediately address the question of euthanasia are nn.2276 - 2279. The intention of the expression "a right to a natural death", as used by Pope Francis, is to articulate in a positive perspective the prohibition of n.2277:
Whatever its motives and means, direct euthanasia consists in putting an end to the lives of handicapped, sick or dying persons. It is morally unacceptable.
And Pope Francis' qualifications - "without aggressive treatment and euthanasia" - equally have a fuller expression in nn.2277 - 2279 of the Catechism, which should be seen as part of how he intends the term to be understood.
However, the term does need to be understood and used carefully. In a clinical context, there is a risk that a direction to "allow natural death" (AND) may in practice be read as a (positively worded) alternative to a direction to "do not resuscitate" (DNR); and, certainly in the UK context, where they are legally seen as a form of treatment and not of ordinary care, it is likely to involve the withdrawal of assisted nutrition and hydration. So, in public discussion, to simply use the term "a right to natural death" without a further specification of your meaning might be unwise.
But, in the context of political, professional and social pressures in favour of euthanasia, the notion that there is an inalienable right (ie a right that cannot be taken away from each and every person) NOT to be subject to euthanasia offers an interesting counter argument to those whose seeking of a legal permission of "assisted dying"/euthanasia threatens to put everyone at risk of pressure to accept euthanasia at the end of their own lives.