The following passages, and there could be more, record being cast into the LOF.
Matthew 25:46 And these shall go away into everlasting punishment: but the righteous into life eternal.
Revelation 19:20 And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone
Revelation 20:10 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 20:15 And whosoever was not found written in the book of life was cast into the lake of fire.
The first question that needs to be asked. Based on what Revelation 20:15 records in regards to not being found written in the book of life, would that also apply to Revelation 19:20 and Revelation 20:10? Of course not. Therefore, those 2 judgments are not involving the same judgment Revelation 20:12-15 is involving, yet they all get cast into the same LOF, but at different times.
Would it also apply to Matthew 25:46 then, in regards to not found written in the book of life? One thing is for certain, Matthew 25:46 is determined during His 2nd coming, not a thousand years later instead. And since they are already judged and sentenced in Matthew 25, does it makes sense that they get judged and sentence again, a thousand years later during the GWTJ? The point being, it could mean some of the unsaved are cast into the LOF prior to the beginning of the millenium, the rest of the unsaved are cast into the LOF after the millennium.
Per my view this can be explained. The goats in Matthew 25 are not meaning all the lost in general, from the beginning of mankind through the end of this age. They are only meaning those in the body of Christ that fell away, thus NOSAS.
Would you agree that Matthew 25:41 refers to people being cast into the lake of fire, also? The same people referenced in Matthew 25:46 are the ones referenced here...
Matthew 25:41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
How about these passages. Do you understand these to be talking about the same thing as the lake of fire, even though Jesus refers to "the furnace of fire" in these?
Matthew 13:40 As therefore the tares are gathered and burned in the fire;
so shall it be in the end of this world. 41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity; 42
And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth. 43 Then shall the righteous shine forth as the sun in the kingdom of their Father. Who hath ears to hear, let him hear.
Matthew 13:47 Again, the kingdom of heaven is like unto a net, that was cast into the sea, and gathered of every kind: 48 Which, when it was full, they drew to shore, and sat down, and gathered the good into vessels, but cast the bad away. 49
So shall it be at the end of the world: the angels shall come forth, and sever the wicked from among the just, 50 And shall cast them into the furnace of fire: there shall be wailing and gnashing of teeth.
Jesus will return at the end of the world/age. That is when He indicated that the wicked will be cast into the furnace of fire, which is just another way of referring to the lake of fire. Jesus also referred to it as "everlasting fire prepared for the devil and his angels" in Matthew 25:41.
So, it seems that you acknowledge that at least some whose names are not written in the book of life will be cast into the lake of fire when Jesus comes again. Yet, Revelation 20:15 does not say that some of those whose names are not written in the book of life will be cast into the lake of fire as of the time that Revelation 20:15 occurs. It just says those whose names are not written in the book of life, which I would say implies all whose names are not written in the book of life. Why would some whose names are not written in the book of life be cast into the lake of fire on one occasion and some on another occasion? What would be the reasoning for that? I don't see any basis for that or any reason why that would be the case.