I think the lake of fire is the method of non-existence -
"... and death and hell were cast into the lake of fire..." Rev 20:14
Rev 21:4- No more death (at all, Isaiah 11:6-9)
Matthew 10:28 "... fear Him who can destroy both soul and body in hell fire"
It is the lake of fire that should be thought of as the ultimate 'hell'
I think one can choose to fight the 'non-existence' and stay 'being' but it is painful. One can also choose to let go and be overcome by the fire and thereby no longer exist. The devil will forever be tormented because he wants everyone to no longer exist, and some will never choose it, rather choosing eternal pain.
Christ experienced a similar thing via death by a cross.
For God will have every righteous reason to judge us, and therefore it must be that He Himself became human, for how can God judge me if He does not know what it is like to be a human and suffer pain?