1 John 5:16
King James Version (KJV)
16If any man see his brother sin a sin which is not unto death, he shall ask, and he shall give him life for them that sin not unto death. There is a sin unto death: I do not say that he shall pray for it.
The man who learns of his brother's sin prays for the brother and God saves the brother.
Salvation is not in veiw here at all. The person that is to be prayed for is called a "brother" not a lost man. The entire book is to provide insights into knowing whether you are saved or lost. John explicitly says this person is a "brother" he does not say "IF one who says they are a brother."
Secondly, the text says nothing of "eternal" life and so that is not only an assumption on your part, but an assumption which contradicts the rest of teaching that clearly says that believers already have "everlasting life" (I Jn. 5:13) at the point they trust in Christ (Jn. 5:24). John wrote both passages and many others declaring that point of present tense eternal life.
Thirdly, can a saved person lose his physical "life" because of open and obvious willful sin? Isn't the purpose of chastening by God to turn a child of God from sin to repentance? Can God increase chastening? Can a child of God commit a sin which costs his physical life?
Should you pray that God will forgive a person who is obviously not repentent in your eyes? Would not it be more proper to pray that God first convicts that person rather than forgive that person? Can physical death be a consequence of willful sin by a child of God?