The OP keeps on insisting that Revelation 14:9-11 is the LOF.
Revelation 14:9 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,
10 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:
11 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.
If the LOF is in view here, and that they have no rest day and night is meaning forever, the text requires that the above has to be undertood like such, based on what verse 10 says.
Before we get to that, look what verse 10 says---The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation
Compare with
Revelation 16:17 And the seventh angel poured out his vial into the air; and there came a great voice out of the temple of heaven, from the throne, saying, It is done.
18 And there were voices, and thunders, and lightnings; and there was a great earthquake, such as was not since men were upon the earth, so mighty an earthquake, and so great.
19 And the great city was divided into three parts, and the cities of the nations fell: and great Babylon came in remembrance before God, to give unto her the cup of the wine of the fierceness of his wrath.
20 And every island fled away, and the mountains were not found.
21 And there fell upon men a great hail out of heaven, every stone about the weight of a talent: and men blasphemed God because of the plague of the hail; for the plague thereof was exceeding great.
Revelation 18:2 And he cried mightily with a strong voice, saying, Babylon the great is fallen, is fallen, and is become the habitation of devils, and the hold of every foul spirit, and a cage of every unclean and hateful bird.
3 For all nations have drunk of the wine of the wrath of her fornication, and the kings of the earth have committed fornication with her, and the merchants of the earth are waxed rich through the abundance of her delicacies.
4 And I heard another voice from heaven, saying, Come out of her, my people, that ye be not partakers of her sins, and that ye receive not of her plagues.
5 For her sins have reached unto heaven, and God hath remembered her iniquities.
Does it sound like the LOF is in view here, in both Revelation 16 and Revelation 18 that I submitted?
Getting back to my point in regard to Revelation 14:9-11. If the 'they have no rest day or night is meaning while they are i the LOF, and is meaning forever, it needs to be understood in this manner then.
and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb, day and night for ever and ever. IOW, they can't be tormented with fire and brimstone unless Christ is present at the time. And if Christ is present day and night for ever and ever as they are being tormented with fire and brimstone, why then does Revelation 21-22 record that Christ is in the NJ day and night for ever and ever instead? How can He be in both places day and night forever and ever at the same time?
Plus, look at the following.
Revelation 14:12 Here is the patience of the saints: here are they that keep the commandments of God, and the faith of Jesus
This is said right after verses 9-11. What in the world does verse 12 have to with the LOF and Revelation 20:11-15?
There are 7 vials of wrath that get poured upon those that have the MOTB. It is during when the vials are being unleashed on them that they have no rest day or night. And that when they are tormented with fire and brimstone in the presence of the Lamb, it is meaning during the 7th vial of wrath, also meaning Ezekiel 38:22. That too involves great hailstones, as does the 7th vial per Revelation 16, and that Ezekiel 38:22 adds this--- and I will rain upon him, and upon his bands, and upon the many people that are with him, an overflowing rain , and great hailstones, fire, and brimstone ---which equals this in Revelation 14:10--- and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:
IOW, Scripture interprets Scripture.