The lake of fire [LOF] is called the second death twice.
Rev 20:14 And death and hell were cast into the lake of fire. This is the second death.
Rev 21:8 But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.
But not one vs. says that anyone/anything is thrown into the LOF then they/it dies in fact just the opposite.
Revelation 20:10
(10) And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
Revelation 21:4
(4) And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.
Revelation 21:8
(8) But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.
If there is no more death after Rev 21:4 then this group does not die.
Revelation 22:11
(11) He that is unjust, let him be unjust still: and he which is filthy, let him be filthy still: and he that is righteous, let him be righteous still: and he that is holy, let him be holy still.
Revelation 22:15
(15) For without are dogs, and sorcerers, and whoremongers, and murderers, and idolaters, and whosoever loveth and maketh a lie.
No more death after Rev 21:4 and last chapter there are still unjust, filthy, dogs, sorcerers, whoremongers, murderers, idolators, and liars outside the new Jerusalem.