False.
The author of the article is reading into Scripture and manifesting his own sin. The scribe who asked Jesus what he needed to do to be saved, since he had kept the Commandments since his birth, was told to give away his possessions and this proved too much a challenge for his fate, might be a candidate for such a false conclusion, but not the report of Lazarus and the rich man.
The reason the rich man was condemned and never received salvation was that he was already condemned from birth, without anything righteous to be identified with God for permanent relationship and because he never submitted to God in his heart, mind and soul, he didn;t even have faith which could be identified with the faith of Christ.
Lazarus did believe and went to Abraham's bosom or Paradise upon his first death. The rich man did not.
The same situation may happen today, but if a rich man today receives Christ through faith in Him, he still has salvation.
Those who are saved might lapse back into sin and arrogance, submitting to the natural man instead of the new man, the new creation, but that doesn't mean their new human spirit will not be saved.
The author hardly presents either a Protestant or Baptist soteriology. Worse, it tends to equate the charity of the believer with salvation. Such a policy results in God being made a debtor, rather than glorifying the Son who has paid the debt in full, allowing God the opportunity to righteously and justly give the believer eternal life by his grace alone.
If faith in Christ is necessary for salvation, then why didn’t Lazarus go to hell, since he never heard of Christ? And why wasn’t he resting in the bosom of Christ, instead of the bosom of Abraham? Sounds as though Jesus was preaching Judaism rather than Christianity!