In Kim, did Kim and the lama die at the end?

I could be very literary here and say that they do, but
not in the sense that you are talking about. Whilst Kim and the lama do not physically
die, they do undergo a kind of death in terms of their former selves dying and being
left behind and being born into a new identity. Let us just remind ourselves what
happens in the final chapter before we look at this
further.

In the final chapter, Kim battles a dangerous
fever. The old woman of Kulu nurses him and he recovers. Mookerjee takes Kim's documents
from him and gives them to the Colonel. Kim at this stage experiences an existential
crisis as he asks "I am Kim. What is Kim?" In a moment of epiphany, however, he comes to
realise that he is finally able to identify himself as belonging to the human race
rather than being estranged from it. The lama narrates to Kim how he has achieved the
Enlightenment he was looking for, having an out-of-body experience that enabled him to
attain the goal of his Search. The novel ends with his claim that he has gained
deliverance from sin for both himself and for Kim.

What is
key to realise is that, while both of these central characters do not die in a physical
sense, their experiences, in particular as related to us in this final chapter, clearly
indicate the way in which they have changed profoundly and in many ways begin new lives
as the novel ends. For Kim, he is finally able to feel that he belongs. The lama
likewise has finally attained the wisdom and deliverance that he has sought for so
long.