Meaning of "dust" when referring to a person
Solution 1:
It means Delilah is dead—long dead. Delilah was younger than the Sphinx, and Delilah has lived her life, died, and rotted away, but the Sphinx is still around, looking as young as she ever did (time has loved her "worthless painted face"—that is, time has not ravaged it the way old age generally does).
'Dust' is used to refer to death because of this passage in the book of Genesis:
In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
That passage is also referenced in the Anglican burial service: "Ashes to ashes, dust to dust." That phrase may be what most English speakers think of when they think of dust in connection with death.
Solution 2:
"Turned to dust" is quite a common phrase for "long dead". In Hamlet, V, i, Hamlet says
Alexander died, Alexander was buried, Alexander returneth into dust; the dust is earth; of earth we make loam, and why of that loam, whereto he was converted, might they not stop a beer-barrel?