In this case, Revelation speaks of a "second death," as it were:
Revelation 2.11: 11 He who has an ear, let him hear what the Spirit says to the churches. He who overcomes shall not be hurt by the second death [τοῦ θανάτου τοῦ δευτέρου].
Revelation 20.6: 6 Blessed and holy is the one who has a part in the first resurrection; over these the second death [ὁ δεύτερος θάνατος] has no power, but they will be priests of God and of Christ and will reign with Him for a thousand years.
Revelation 20.14: 14 And death and Hades were thrown into the lake of fire. This is the second death [ὁ θάνατος ὁ δεύτερος], the lake of fire.
Revelation 21.8: 8 But for the cowardly and unbelieving and abominable and murderers and immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death [ὁ θάνατος ὁ δεύτερος].
Revelation 20.6: 6 Blessed and holy is the one who has a part in the first resurrection; over these the second death [ὁ δεύτερος θάνατος] has no power, but they will be priests of God and of Christ and will reign with Him for a thousand years.
Revelation 20.14: 14 And death and Hades were thrown into the lake of fire. This is the second death [ὁ θάνατος ὁ δεύτερος], the lake of fire.
Revelation 21.8: 8 But for the cowardly and unbelieving and abominable and murderers and immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death [ὁ θάνατος ὁ δεύτερος].
It is not at all clear what this term means from its first appearance in this book, but the other three explain. To die a first death is to die to this present life; to die a second death is to die to the life to come: to spend eternity in the lake of fire instead of in God's presence.
The Talmud is familiar with a similar concept:
Talmud, Sanhedrin 92a: 92a .... Raba said: "Whence is resurrection derived from the Torah? From the verse, 'Let Reuben live, and not die,' meaning, let Reuben live in this world, and not die in the next." Rabina said, "From this verse, 'And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt.'" Rabbi Ashi said, "From this verse, 'But go thou thy way till the end be; for thou shalt rest and stand in thy lot at the end of the days.'" ....
Deriving the doctrine of resurrection from Daniel 12.2 and 12.13 is no feat, but to derive it from Deuteronomy 33.6 is a bold stroke. To "die in the next" world seems to mean not to be able to participate in the world to come, just as to die in this world means no longer to be able to participate in this world, this life.
But the exact term, "second death," does not appear here. It does, however, appear in the Targum to that very same Deuteronomic verse which Raba interprets above (while bravely playing that favorite rabbinical game of finding proof of the resurrection in the Pentateuch, which notoriously lacks anything clear on that topic):
Deuteronomy 33.6 Masoretic: 6 "May Reuben live and not die, nor his men be few."
Targum Jerusalem, Deuteronomy 33.6: 6 Let Reuben live in this world, nor die the second death which the wicked die in the world to come; and let his youths be with the men in number.
Targum Onkelos, Deuteronomy 33.6: 6 Let Reuben live in life eternal, and not die the second death; and let his children receive their inheritance according to their numbers.
Targum pseudo-Jonathan, Deuteronomy 33.6: 6 Let Reuben live in this world, nor die the second death which the wicked die in the world to come; and let his youths be numbered with the young men of his brethren of Beth Israel.
Targum Jerusalem, Deuteronomy 33.6: 6 Let Reuben live in this world, nor die the second death which the wicked die in the world to come; and let his youths be with the men in number.
Targum Onkelos, Deuteronomy 33.6: 6 Let Reuben live in life eternal, and not die the second death; and let his children receive their inheritance according to their numbers.
Targum pseudo-Jonathan, Deuteronomy 33.6: 6 Let Reuben live in this world, nor die the second death which the wicked die in the world to come; and let his youths be numbered with the young men of his brethren of Beth Israel.
The meaning here is clearly identical to the meaning of the term in Revelation.
Other Targumim are involved, as well:
Isaiah 22.14 Masoretic: 14 But Yahweh of hosts revealed Himself to me, "Surely this iniquity shall not be forgiven you until you die," says the Lord God of hosts.
Targum Isaiah, Isaiah 22.14: The prophet said, "With my ears was I hearkening when this was decreed before Yaway of hosts, 'This sin shall not be forgiven you till you die the second death,' says Yaway of hosts.
Isaiah 65.5-6 Masoretic: 5 "Who say, 'Keep to yourself, do not come near me, for I am holier than you!' These are smoke in My nostrils, a fire that burns all the day. 6 Behold, it is written before Me, I will not keep silent, but I will repay; I will even repay into their bosom.
Targum Isaiah, Isaiah 65.5-6: Their punishment shall be in Gehenna, where the fire burns all the day. Behold, it is written before me, "I will not give them respite during life, but will render them the punishment of their transgressions and will deliver their body to the second death."
Isaiah 65.15 Masoretic: 15 "And you will leave your name for a curse to My chosen ones, and the Lord God will slay you. But My servants will be called by another name.
Targum Isaiah, Isaiah 65.15: And you shall leave your name for a curse to my chosen and Yaway God will slay you with the second death, but his servants, the righteous, he shall call by a different name.
Jeremiah 51.39 Masoretic: 39 "When they become heated up, I shall serve them their banquet and make them drunk, that they may become jubilant and may sleep a perpetual sleep and not wake up," declares Yahweh.
Targum Jeremiah, Jeremiah 51.39: 39 "I will bring upon them distress and they shall be like drunken men so that they may not be strong and they shall die the second death [תִניָנָא וִימֻותֻון מוֹתָא] and shall not live in the world to come."
Jeremiah 51.57 Masoretic: 57 "And I shall make her princes and her wise men drunk, her governors, her prefects, and her mighty men, that they may sleep a perpetual sleep and not wake up," declares the King, whose name is Yahweh of hosts.
Targum Jeremiah, Jeremiah 51.57: 57 ...and they shall die the second death [וִימֻותֻון מוֹתָא תִניָנָא] and shall not come to the world to come.
Targum Isaiah, Isaiah 22.14: The prophet said, "With my ears was I hearkening when this was decreed before Yaway of hosts, 'This sin shall not be forgiven you till you die the second death,' says Yaway of hosts.
Isaiah 65.5-6 Masoretic: 5 "Who say, 'Keep to yourself, do not come near me, for I am holier than you!' These are smoke in My nostrils, a fire that burns all the day. 6 Behold, it is written before Me, I will not keep silent, but I will repay; I will even repay into their bosom.
Targum Isaiah, Isaiah 65.5-6: Their punishment shall be in Gehenna, where the fire burns all the day. Behold, it is written before me, "I will not give them respite during life, but will render them the punishment of their transgressions and will deliver their body to the second death."
Isaiah 65.15 Masoretic: 15 "And you will leave your name for a curse to My chosen ones, and the Lord God will slay you. But My servants will be called by another name.
Targum Isaiah, Isaiah 65.15: And you shall leave your name for a curse to my chosen and Yaway God will slay you with the second death, but his servants, the righteous, he shall call by a different name.
Jeremiah 51.39 Masoretic: 39 "When they become heated up, I shall serve them their banquet and make them drunk, that they may become jubilant and may sleep a perpetual sleep and not wake up," declares Yahweh.
Targum Jeremiah, Jeremiah 51.39: 39 "I will bring upon them distress and they shall be like drunken men so that they may not be strong and they shall die the second death [תִניָנָא וִימֻותֻון מוֹתָא] and shall not live in the world to come."
Jeremiah 51.57 Masoretic: 57 "And I shall make her princes and her wise men drunk, her governors, her prefects, and her mighty men, that they may sleep a perpetual sleep and not wake up," declares the King, whose name is Yahweh of hosts.
Targum Jeremiah, Jeremiah 51.57: 57 ...and they shall die the second death [וִימֻותֻון מוֹתָא תִניָנָא] and shall not come to the world to come.
The casual way in which Revelation 2.11 throws in the concept of a second death without explaining it suggests that John the Revelator was drawing upon an established line of thought; I doubt he invented the term and then the Targumists later borrowed it from him.
Ben.