The second death, (the lake of fire) does not have the power to kill... only to hurt.
Revelation 2:11 He that hath an ear, let him hear what the Spirit saith unto the churches; He that overcometh shall not be hurt of the second death.
The word 'hurt' is translated from the Greek word 'adikeo.' The Greek word 'adikeo' is never translated as kill or killed.
We further see that the wicked are not killed when we read Revelation 14:9-11
Revelation 14:9-11 And the third angel followed them, saying with a loud voice, If any man worship the beast and his image, and receive his mark in his forehead, or in his hand, The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb: And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
Paul tells us in 1 Corinthians 15 that the 'last enemy to be destroyed is death.'
1 Corinthians 15:26 The last enemy that shall be destroyed is death.
Notice that Paul did not say, 'second death.' Second death, (the lake of fire will not be destroyed. Second death will be the instrument that is used to destroy death.
Revelation 20:13-15 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works. And death and hell were cast into the lake of fire. This is the second death. And whosoever was not found written in the book of life was cast into the lake of fire.
Notice that before the wicked are cast into the lake of fire, death and hell are cast in. The last enemy to be destroyed is death. The lake of fire destroys death. When the wicked are subsequently cast into the lake of fire, they can only be 'hurt' (Rev. 2:11) by the lake of fire, not killed by it for death has been destroyed.
They will experience eternal torment. They will have no rest for ever and ever.