Sri Aurobindo translates Katha Upanishad, First Cycle, First Chapter, Verses 7 to 9: “His attendants say to Yama: ‘Fire is the Brahmin who enters as a guest the houses of men; him thus they appease. Bring, O son of Vivasvan, (Yama, lord of death, is also the master of the Law in the world, and he is therefore the child of the Sun, luminous Master of Truth from which the Law is born.) the water of the guest-rite. That man of little understanding in whose house a Brahmin dwells fasting, all his hope and his expectation and all he has gained and the good and truth that he has spoken and the wells he has dug and the sacrifices he has offered and all his sons and his cattle are torn from him by that guest unhonoured.’ Yama speaks: ‘Because for three nights thou hast dwelt in my house, O Brahmin, a guest worthy of reverence, — salutation to thee, O Brahmin, on me let there be the weal, — therefore three boons do thou choose, for each night a boon.’ ”
The interaction between Nachiketas and Yama the Lord of Death and the law of life, is clearly symbolic and esoteric. These verses bring in the traditional prescriptions for householders to treat the unexpected guest as god, and to care for and feed that guest with all due reverence. Such a prescription placed upon human beings does not translate to the Lord of Death when people enter his abode. It is meant however to convey specific information to the seeker and to provide a transition to bring about the 3 questions and the 3 boons which are the substance of this Upanishad.
We see in occult traditions that death involves the dissolution of the elements of the body, life force and the mind, step by step, as the ego, acting as the lynch-pin, lets go of these elements. Here we are dealing with the spiritual experience of death, which involves the release of the ego consciousness and the corresponding psychological elements of the attachment to the chain of cause and effect (karma) and the action of desire (kama).
In The Tibetan Book of the Dead, the passage from life into death and back into rebirth involves a process of physical time in the external world. It is not simply a matter that all the elements dissolve immediately upon death of the body. Even the process of transitioning to the new standpoint inwardly is not something that is completed immediately. The bonds of desire and attachment have to fall away, the ego has to lose its control over the consciousness and a shift has to occur to the new psychological experience. Fasting for three days is a traditional action used to undertake the release of desire and attachment to karmic action, and thus, bringing this element in helps the seeker to understand what is required to truly confront the law of life and death and gain the deeper understanding that the Upanishad intends to convey.
Sri Aurobindo, The Upanishads, Katha Upanishad, pp. 213-241, and Kapali Sastry, Lights on the Upanishads, pp. 104-129