One of my questions, or points to ponder, concerning this question is, what was the perception concerning the second resurrection and what did they see as being the requirement in order to be written in the Lamb's Book of Life.
To me, it's the very first Christians only, because even at the time of the writings of the New Testament letters, there were untruths of doctrine circulating. Today most churches or groups believe one becomes saved by saying a "sinner's prayer" asking Jesus into their heart, which by all means is not a bad thing! But Jesus said, and Paul also later wrote, that if one "believed Jesus was the Son of God, and believed that He rose from the grave" (truly believed, with changes in character and life becoming evident) they were saved (adopted) and became "the children of God".
The other point to ponder along with this, is, what exactly did Jesus mean (and how did the disciples hear it) when He said to some Scribes and Pharisees "you will die in your sins". Many assume that means case closed, die in your sins before repenting and receiving and believing the truth of Jesus, and you are forever in that state. Yet is this how the disciples heard and perceived this. It is much more logical that what was being stated and understood here, was that the first resurrection (of believers "putting on immortality") far exceeds the second resurrection of still being imperfect (in one's own flaws, blindness, etc) during what is very likely (?) a very long day of the examination of all things, wherein "He will judge the living"(1st resurrection), "and the dead"(2nd resurrection, imperfect is the opposite of God thus opposite of life). I can't help but take this to mean that all of human history will be examined (as to what went wrong in all generations and peoples, etc..)
When did the apostles and first christians believe the Lamb's Book of Life became closed and nary another name written therein? When slammed shut and no other name could be added? No one able to "believe". Before Judgment/Examination Day? Or..
Where are the scriptures that explicitly say, "receive the truth of Jesus before you die or all is forever lost"..? Wouldn't that be very highly and often mentioned if it were true and perceived as true by the apostles? And also by our Lord Himself? Wouldn't it be such a critical message, it would be weaved throughout all teachings, speeches and writings of the apostles?