On one hand, some think a thunderbolt thrown by Zeus could kill even those who are born immortal like Menoetius, “Now Iapetus took to wife the neat-ankled maid Clymene, daughter of Oceanus, and went up with her into one bed. And she bare him a stout-hearted son, Atlas: also she bare very glorious Menoetius . . . But Menoetius was outrageous (hubristic), and far-seeing Zeus struck him with a lurid thunderbolt and sent him down to Erebus because of his mad presumption and exceeding pride. “ (Hesiod, Theogony 507) or Typhon; “Zeus…seizing his weapons, thunder, lightning, and the glowering thunderbolt, he made a leap from Olympus, and struck...Then, when Zeus had put him down with his strokes, Typhoeus crashed, crippled, and the gigantic earth groaned beneath him… Zeus in tumult of anger cast Typhon into broad Tartarus.” (Hesiod, Theogony 820)
On the other hand, at least one mortal, Anchises, survives a thunderbolt without divine help; “Venus is said to have loved Anchises and to have lain with him. By him she conceived Aeneas, but she warned him not to reveal it to anyone. Anchises, however, told it over the wine to his companions, and for this was struck by the thunderbolt of Jove” (Hyginus, Fabulae, 94) Indeed, for he was, like the river “Asopos, heavy-kneed, for he was marred by a thunderbolt." Callimachus, Hymn 4 to Delos 75)
The death of the Cyclops really pushes the whole question. Can you kill an immortal? Is there a crucial difference between being a subterranean worker and being dead in Hades? "Zeus was afraid that men might learn the art of medicine from Asclepius and help each other out, so he hit him with a thunderbolt. This angered Apollo, (his divine father) who slew the Cyclopes, for they designed the thunderbolt for Zeus. (Pseudo-Apollodorus, Bibliotheca 3. 118 – 122) Were these the elder Cyclopes? The three, single-eyed, immortal giants who forged the lightning-bolts of Zeus; sons of Father Uranus and Mother Gaea? Or the fellow tribesmen of Polyphemus, son of Poseidon and Toosa? Or others who survived like the Basque Cyclops Tartaro. And just to confuse the issue Asclepius, returned to earth as a god.
The Hesiodic reference to Menoetius’ life is short, but Aaron J. Atsma makes him later the herdsman of Hades, whom Herakles wrestled with in the underworld. (Theoi Project Copyright) Wasn't Typhon buried under Etna? At least according to Prometheus, who says of the monster (Aeschylus, Prometheus Bound 353)”, a helpless and a sprawling bulk, he lies hard by the narrows of the sea, pressed down beneath the roots of Aetna” That's why in Hesiod the Titans are "bound" in Tartarus; whether struck by lightning or tossed into the pit, so they cannot escape. Likewise, no mortal dies in Greek myth; their souls go to Hades; their immortal parts go to some version of the Isle of the Blest or Olympus. No one actually dies, it is just an illusion poorly maintained by the gods in order to insure their rule.
The above paper evolved from a conversation by WilliamMoulton2 and Maya M.Inspired by TFBT: Saving the Drown Toddler Glaucus