What is the lesson from Cornelius for the church today?

The lesson is that religious devotion, sincerity, prayer, and giving are not salvation; many church people resemble Cornelius—devout yet unsaved—until they hear and believe the words Peter preached. Salvation comes by the message, not by good works or religiosity.

Les teaches that Cornelius was devout, prayed, gave alms, and believed in God, yet he was still lost. The angel told him to send for Peter, who would tell him words whereby he and all his house would be saved—future tense, showing they were not saved yet. The lesson is the same today: churches are full of people like Cornelius who are devout, sincere, pray, and give, but are lost. It is a sad but true picture.

Acts 10:2

A devout man, and one that feared God with all his house, which gave much alms to the people, and prayed to God alway.

Was Cornelius already saved even though he was devout and feared God?

No. Though Cornelius was a devout Roman officer who feared God, gave alms, and prayed to the true God, he is described as lost. Religious devotion and prayer to the right God did not save him; he still needed the gospel.