Can "to close one's eyes" mean "to die"?
A negative is hard to prove definitively, but no,
to close one's eyes
all by itself does not metaphorically refer to one's death.
In the context of that phrase "Man’s entire life", sure, it makes sense as a metaphor, but 'to close one's eyes' is not a set phrase that refers to death in general.
And yes your dictionaries are right in that
to close one's eyes to something
means, in a slightly different metaphor, to intentionally ignore or forget about something.