The key is understanding that there are two lakes in the book of Revelation.
The lake of fire is the second death. Hades and death were thrown into this lake. Their role was finished, so the lake of fire is permanent destruction. This lake is the destination of the people whose names are not written in Jesus’ book of life. For them it was annihilation (Rev 20:14-15). This fire burns purely, so it is the work of God.
The destination of the beast and the false prophet is different. They go into a lake of burning sulphur. Sulphur is often caused brimstone. It eats away at flesh and destroys it slowly. It was often used in rubbish dumps to destroy organic material.
In Revelation, sulphur is associated with the powers of evil. The evil spirit that came out of the Abyss spat out fire and sulphur (Rev 9:17-18). Sulphur stinks, which also reminds us of evil.
The fiery lake of burning sulphur is a place of torment (Rev 20:10). The Beast and the false prophet are tormented day and night. It is a place set up by the spiritual powers of evil as an imitation of the real thing, but with an evil twist. Torment replaces annihilation. The powers of evil set it up so they can torment other spirits that have betrayed them.
Christians who believe in eternal conscious torment of those who reject the gospel have confused the two lakes. God allows people who have rejected the gospel to be destroyed, if they do not want to be with him. He does not torment people. That is what the evil spirits do.