Surely you notice that "day and night" are still going on in this environment. That means this is a location on earth where the living inhabitants are being tormented - not the Hadean realm for the wicked dead. And the worship given to the Sea Beast and its image is still going on in this scenario as well.
The "Lake of Fire" / aka the "second death" was the second death of the city of Jerusalem and its temple, and the end of Israel as a "holy people" at that "end of the age". This took place during the AD 66-70 period. That "furnace of fire" (Matt. 13:42) was in the city of Jerusalem (as the prophet said in Isaiah 31:9). The living, besieged inhabitants of Jerusalem in those years certainly were "tormented" during the "latter end" of Israel as a people.
Scripture describes the weeping and gnashing of teeth by these individuals, and their protesting plea to the returning Christ, "We have eaten and drunk in thy presence, and thou hast taught in our streets." Only the first-century generation of Jewish citizens could possibly utter this statement. It was that first-century generation and their children who Christ warned that, instead of weeping for Him, they should weep for themselves and their children for what was personally going to come upon them during their lifetime.
This torment of the first-century Israelite citizens besieged in their own city Jerusalem should not be interpreted as the after-life perpetual fate of the wicked.
Not on the earth, but under the earth.
The Lake of fire is uninhabited as of yet.
The Lake of fire is where all the lost are cast:
Revelation 20:7-15
King James Version
7 And when the thousand years are expired, Satan shall be loosed out of his prison,
8 And shall go out to deceive the nations which are in the four quarters of the earth, Gog, and Magog, to gather them together to battle: the number of whom is as the sand of the sea.
9 And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them.
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.
11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.
12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
13 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.
14 And death and hell were cast into the lake of fire. This is the second death.
15 And whosoever was not found written in the book of life was cast into the lake of fire.
Gehenna is a name for the place of torment where all lost are being held for now.
Just because you see furnace of fire does not equate it to the lake of fire. That is bad hermeneutics.