Yes, God does indeed keep those who go to hell and the lake of fire in a state of eternal torment. Understand that they made that choice. They chose that. They had another option to go to heaven, but they rejected that option. Likewise those who make it to heaven remain in a state of eternal bliss.
Those who make it to hell and later on to the lake of fire they will exist always in that location(s) Bible says God is with us always even if we make our bed in hell. God never forgets who anyone is. The choice you make is the choice you get. Read what I posted earlier about Lazarus. God is talking to the rich man while he is in hell -not forgetting who he is, but actually talking to him.
Psalm 139:8 If I ascend up into heaven, thou art there: if I make my bed in hell, behold, thou art there.
That's Dante not scripture.