Agreed, in the sense of that there is no particular duty
for the lawyer(s) to notify relatives of the bare fact of death.
That is typically a job for the family.*
However, if it turns out that his will is (wholly or partially) invalid,**
and therefore must be dealt with as an intestacy, or,
if they are entitled to bring a Family Provision claim,***
then it can be different.
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* That being said, the testator (in their will or in other
ante mortem instructions),
or the family, or the executor, might ask a lawyer to do it (as lawyers "pursuant to instructions").
This could happen as matter of convenience, or if family members themselves are prevented from doing so
perhaps by reason of health, distance, estrangement, or by legal disability (say, imprisoned), or
otherwise prevented operation of law - such as an AVO not permitting contact.
** Such as, but not only, if he did his will on a DIY form from a newsagent, and in some way, got it wrong,
or, if there are questions about his capacity ifhe made a new will late in life.
*** The prospects of success of any such claim being a separate question