Lutherans believe we are still sinners and we will always be sinners until the day we die. However, those who place their faith in Christ and repent, are sinners-saved-by-grace, and will inherit eternal life in heaven.
Please show me one verse in the Bible that states that one must know a time in the past that they "were" a sinner in order to be a Christian.
You have answered your own question when you said:
"those who place their faith in Christ and repent" and this is precisely what the scripture repeat over and over again by precept and by example.
However, your concept of NEVER experiencing a time in one's life of ever beleiving or repenting and yet still be saved contradicts that very statement and indeed is a contradiction in terms. If there was never a time you experienced a lost condition then it could only have occurred when one came to that realization NOT BEFORE!
What is necessary is that one know that he IS a sinner, lost and bound for hell, without the free gift of salvation offered by Christ to all those who place their faith in him, believe in Him, and repent.
That is the point, your hypothetical example HAS NO CONSCIOUSNESS OF SUCH A PAST CONDITION. Whatever point in time they grasped that concept is the time they were saved and not a moment before.
They may not remember the day or hour but they MUST remember the EXPERIENCE or they have NO WITNESS of salvation and they are not saved yet.