The planet earth will remain the planet earth, but everything on its surface will be burned up to make way for the New Earth.
You are quite mistaken about the Lake of Fire. First of all it was created long ago for the Devil and his angels, and secondly it is in "outer darkness" which definitely means not on earth but even outside of space (which is finite).
Joh 14:2 In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.
Joh 14:3 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.
Jesus went away to prepare a place for the saints,which is the final destination of the saints,so it is not of this earth.
2Pe 3:10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
2Pe 3:11 Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness,
2Pe 3:12 Looking for and hasting unto the coming of the day of God, wherein the heavens being on fire shall be dissolved, and the elements shall melt with fervent heat?
2Pe 3:13 Nevertheless we, according to his promise, look for new heavens and a new earth, wherein dwelleth righteousness.
God will create a new heaven and a new earth,and the former heaven and earth shall be on fire and be dissolved for they are associated with sin and rebellion,and all sin must be purged with fire,and the new heaven and earth will be a place wherein dwells righteousness,for it will be a place where sin has never been and sin will never be,where the former heaven has been tainted by Lucifer and the fallen angels when they rebelled,and the earth tainted with sin by rebellious people,so they must pass away.
Rev 21:1 And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea.
Rev 21:2 And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband.
Rev 21:3 And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.
Rev 21:4 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.
Rev 21:5 And he that sat upon the throne said, Behold, I make all things new. And he said unto me, Write: for these words are true and faithful.
The first heaven and earth passed away,and the former things have passed away,and Jesus makes all things new.
The earth and heaven have been tainted with sin,and cannot be redone,or refurbished,but must completely pass away,and sin and rebellion has been on earth,and the new heaven and the new earth is a place where sin has never been and sin will never be,for all things are new.
Isa 65:17 For, behold, I create new heavens and a new earth: and the former shall not be remembered, nor come into mind.
When the saints and angels are at the New Jerusalem this earth and heaven shall not be remembered,nor come to mind,for they are associated with sin and rebellion,and the saints and angels will remember nothing prior to the New Jerusalem,but will feel as if they have always been there and nowhere else.
For the saints and angels to remember this earth and heaven they would have to have the knowledge of sin and rebellion that occurred there which God does not want them to know,but they will only know the ways of the Lord and that is it.
Zec 14:9 And the LORD shall be king over all the earth: in that day shall there be one LORD, and his name one.
Jesus said until heaven and earth pass away not one jot or tittle shall pass from the law until all is fulfilled,and when Jesus fulfills the role of King on earth in the millennial reign of Christ then the law has been fulfilled,and heaven and earth shall pass away and be no more.
What would a surface cleaning do to earth that has been tainted with sin,but she must completely pass away.
Psa 63:9 But those that seek my soul, to destroy it, shall go into the lower parts of the earth.
Psa 55:15 Let death seize upon them, and let them go down quick into hell: for wickedness is in their dwellings, and among them.
Pro 15:24 The way of life is above to the wise, that he may depart from hell beneath.
Amo 9:2 Though they dig into hell, thence shall mine hand take them; though they climb up to heaven, thence will I bring them down.
Act 2:31 He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.
Act 2:32 This Jesus hath God raised up, whereof we all are witnesses.
Death and hell is below in the lower parts of the earth.
Rev 20:13 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.
Rev 20:14 And death and hell were cast into the lake of fire. This is the second death.
Death and hell were cast in to the lake of fire which means the whole earth shall go in to the lake of fire.
This heaven and earth will be no more one day and will be dissolved like alka seltzer in water,and there will be a new heaven and a new earth.