Nobody is sent to the Lake of Fire because of any judgment of personal sin. ALL sin has been judged at the Cross.
We all stand condemned, until we exercise faith in Christ at the Cross. When we accept the judgment of those sins at the Cross and confess our acceptance of that payment for our sins, then we are forgiven and He gives us eternal life.
Every human being begins condemned (except Adam and the 2nd Adam). The Judgment of all sin has now occurred some 2000 years ago.
You are right, the determining factor is whether a person’s name is found in the Lamb’s Book of Life. If not found, that person is thrown in the Lake of Fire. And we get our names in the Book by faith in Jesus and His work at the cross. The point I was trying to make in my previous post was that any sin is the same to God, deserving of eternity in the Lake of Fire, regardless of how “bad” or how “small” the sin is. It is not confession, purgatory or anything like that that saves us, but grace through faith.