Jesus said, from Luke 12:49-53:
“I have come to bring fire on the earth, and how I wish it were already kindled! But I have a baptism to undergo, and how distressed I am until it is completed! ...”
The baptism that Jesus had to undergo was the baptism of His suffering of pain and death that He was soon to do on the cross.
After the death and resurrection of Jesus were done, He would never have anything to do with such a baptism again.
The pain and death were done. But such is the power of the God part of Jesus, that the pain and death would become, in itself, a fire. This fire would start in the hearts of all people, regarding whether or not they believed in Jesus salvation.
The final end of the fire will be the Lake of Fire talked about in the Revelation. Revelation 20:14,15:
Then death and Hades were thrown into the lake of fire. The lake of fire is the second death. If anyone’s name was not found written in the book of life, he was thrown into the lake of fire.
The lake of fire, the culmination of all the work that Jesus did on the cross, is the evil of the world being destroyed. Even death and hell will be dissolved in the lake of fire, so that there will be no death anymore.
Along with all the rest of the evil, will be the people whose names are not found in the Book of Life. They, also, will be thrown into the lake of fire.
So, what exactly is the lake of fire for? God is so great that He is not effected by eternity. He is way beyond things like infinity and eternity, although He works with them, and even takes part of them at times.
The lake of fire is the "smelting furnace" where all the evil will be smelted down into its basic form. God gave goodness. It turned itself into evil in many cases. The lake of fire converts the evil into its basic format so that God gets his power back, purified into good again.
If you and I are saved, our goodness (applied goodness coming from Jesus, and accessed by us through our faith in Jesus) will remain forever with God in Heaven.
Our evil was taken by Jesus on the cross, and is, along with Jesus death, stuff that makes up the greater part of the lake of fire. The devil and his angels make up part of the lake of fire. And all those people whose names are not found in the book of life will make up part of the lake of fire. The universe will be tossed into the lake of fire, because it is all corrupted by evil - the universe is one; it is corrupted by having evil in it.
BTW, there will be a new universe - Revelation 21:1: "Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and there was no longer any sea." - created without any evil or corruption in it. The word "sea" refers to the devil, and the body of people whose names were not written in the Book of Life.