Christian actions manifest holy sanctification and faith.
But not every name is written in the Book of Life.
Right. My argument.
All the others are named in "other books" and are condemned to the second death.
How come, if Jesus Christ supposedly removed all the sins of all men?
God's forgiveness of ALL sins was paid for and that act is implemented to all those who hear the True Gospel and place their faith in Christ. If one chooses to reject God's Grace they will not inherit eternal life. There will not be anyone cast into the Lake of Fire because of their sin. They will be judged by their deeds and their rejection of God's free gift of eternal life through faith in the death, resurrection, and Diety of the Lord Jesus Christ as their Savior.