Since the Great White Throne Judgment takes place following the destruction of our current heavens and earth and arrival of the new heavens and earth (Revelation 20:11), where is the location of the Lake of Fire?
The Lake of Fire's specific location is never given in scripture, though we find an important clue in Revelation 14:
Rev. 14:9 Then another angel, a third one, followed them, saying with a loud voice, “If anyone worships the beast and his image, and receives a mark on his forehead or on his hand,
Rev. 14:10 he also will drink of the wine of the wrath of God, which is mixed in full strength in the cup of His anger; and he will be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb.
Notice the location of the place of eternal torment is said to be "in the presence of the holy angels and in the presence of the Lamb.” This description would imply that the Lake of Fire will be located in the heavenly places, not in the physical realm. Therefore, it's existence is not impacted by the destruction of the first heavens and earth following the 1,000-year kingdom, since it is not a part of the created universe.
Beyond this, we cannot say where the Lake of Fire exists.