According to the legendarium
It was a tradition under the Eldar and Edain that they [Idril and Tuor]Túor] arrived in Valinor, and that TuorTúor alone of Men was counted among the Eldar, immortal as other Elves.
but also, after Beren's death
[In Mandos] [Luthien][Lúthien] sang a song of woe before the throne of Mandos Lord of the Dead... As a result he summoned Beren from the houses of the dead.
and
Even Manwë could not change the fate of Men, and so he presented Lúthien with the [] choice [] to return to the land of Middle-earth together with Beren as a mortal herself, accepting the Doom of Men and sharing in whatever unknown fate awaits them outside the Circles of the World.
According to the citation on Tolkien Gatewaycitation on Tolkien Gateway, Tolkien confirms that TuorTúor being granted immortality was a unique exception by the special will of Ilúvatar himself - Eru being the only one capable of taking/giving the the gifts of Mortality and Immortality, which were gifts from Eru to the Eruhini - in Letter #153.
But then we have the Valar recalling Beren's spirit and bringing it back to life (for a limited time) and giving the 'Gift/Doom' of Mortality to LuthienLúthien, without any hint of intervention by Eru.
Is there any info in Tolkien's letters or in any other publications regarding this?
How were the Valar able to take away Luthien'sLúthien's immortality and give her mortality, when apparently that's the purview of Eru alone? (How did Beren's dead soul turn up in Mandos, when he should have suffered the Doom of Men and how did the Valar have the authority to send it back to MEMiddle-earth even on a temporary basis?)
Edited to add the cases of LuthienLúthien and Beren as well, because this all seems extremely related and possibly one question.