Answer:It did not say that Cornelius was lost at anytime, He was under the Old Law, and would be justified till he knew the truth. We lost Cornelius when God does not. If he had not responded to God message and been obedience to Peter's preaching, then he would have been lost. I know you are going to say the he was told that he could be saved, but that was under the Church age that had started.
Have a great day, but let God be the judge.
"And he told us how he had seen an angel standing in his house, who said to him, 'Send men to Joppa, and call for Simon whose surname is Peter, who will tell you words by which you and all your household will be saved.'" (Acts 11:13-14).
If Cornelius was not lost, then from what was he being saved? You stated that he lived under the Old Testament law, but that too is untrue. Cornelius and his household were uncircumcised Gentiles (Acts 11:3), as such they were excluded from the promise of the covenant. "Therefore remember that you, once Gentiles in the flesh--who are called Uncircumcision by what is called the Circumcision made in the flesh by hands-- that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world." (Ephesians 2:11-12). Cornelius was not saved under the Old Law. At the time that God visited him, Cornelius needed saving, so therefore he wasn't saved at that time, even though he did not yet hear the gospel message and did not have a chance to reject it. Since it was God who said Cornelius needed to be saved, it was God who had judged.
I don't know if you have thought this through or not, but by saying that Cornelius was saved until he heard the gospel and rejected it, you have turned the point of the gospel upside-down. Instead of being the means by which a lost person can be saved (Romans 1:16), you are saying that for at least one person it was the means by which a saved person could be lost.
The above note was sent in response to the first lesson on Cornelius. You may click here to read the lesson.