Does Lucifer torment the sinners out of his own will or God's will?

The devil doesn't torment anybody in hell. The devil will be tormented in hell. So the first point is false. The devil hates everybody.
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Jesus loves you and wants to bless your life freely :) Most of all, Jesus wants you with Him forever, and not in hell. The truth is that every belief except one will lead to eternal torment in the lake of fire for every person. Because nothing pays for our sins except the death and blood of Jesus, the sacrifice of Jesus that is already accomplished by Him . Jesus loves you! The truth is that Jesus is God, and Jesus died on the cross to pay for all of our sins in full, and then Jesus resurrected from the dead. Nothing else pays for our sins, not works, not deeds, not religions. So the only way to heaven and to avoid hell, is by believing in Jesus for eternal life (John 6:47), without adding any of your own works (Romans 4:5). Believe in Jesus to take you to heaven, and you will be in heaven, no matter what, guaranteed. That easy, thanks to Jesus! Tell Jesus that you thank Him that you will be with Him in heaven when you die, because you believe in Jesus! It is too late to be saved, after death

That "FRUIT" looks GOOD doesn't it "EVE?"!!!

You don't know the Bible. Satan doesn't rule in hell.

Revelation 20:10
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.

Lucifer doesn't torture sinners. The sinners will mentally torture themselves due to their loss of a happy eternal life. God will look upon them in disgust for all eternity.

Where did you ever get such nonsensical ideas as these?

The idea that the devil torment people in hell and that the demons are free to go around torturing people in hell with pitchforks and other means of torture is simply untrue. What you're going to find when you get to hell is 4 1/2 ft deep melted sulfur it's on fire the fire is about a foot-and-a-half tall it's bluish in color yellowish red clouds a fumes pour off of the sulfur. I can't tell you what's worse the pain of standing in burning glue that has sulfuric acid building up in it or choking constantly. But I can tell you that everybody devil demons and those sentenced to hell are powerless to do anything at all except stand in one place because of the thickness of the crap that's there and scream in pain. there's no sex parties there's no snakes there's no drugs there's no alcohol there's no water there's no food nothing but fire and screaming forever and ever. And the devil won't be trying to hurt you because he'll be in too much pain just like everybody else.

We can see that in Job, Satan goes before God. There, God asks him a provoking question: "Have you seen my servant Job?". We can see that Satan answers and yes, has already been testing the hedges of protection around him that God had made. This was something God had put in place from the wild youth of Job and his and God's grown relationship. Satan could not harm him also as God had not given him permission, but we see that it was Satan's desire, not God's. However, to prove to Satan his servant's righteousness, and once more show Satan they would not win, he allowed him to proceed with limitations. It was his desire, not God's. It was God's desire to use the evil of Satan to later bless Job and show him a greater understanding of who God is and why he does what he does. Not only that, but Job became a sign for all the rulers, kings, his family, and his friends of that time. Furthermore, he's been a sign to each person since the event had been documented. All of this was born out of Satan's evil and God's masterful ability to turn that evil to goodness. Job's children who died were preserved by his prayers to cover their sins, and despite it being sad that they were dead, he was blessed all the more later with countless herds and offspring.

Lucifer is like the guy who drops out of school and then sees an intelligent person whit a good future threaten to do the same thing

his own

The only time Lucifer was ever depicted tormenting anyone, it was God's idea in the first place and for no valid reason.