Yes, a person in a state of grace can lose that state through mortal sin. I read 1 John 5:20 and Ephesians 2:6 as describing the gift of eternal life, not its guarantee against apostasy. I'd lean into [CCC 1428-1429] on 'second conversion' as an ongoing, lifelong process for baptized Christians. It's not a one time event but an uninterrupted process for the entire Church in need of continual purification and a response to God's mercy and love. "St. Peter's conversion after he had denied his master three times bears witness to this."
One thing I love about the Catholic Church is that they provide the Catechism as a reference to the churches teachings; free and openly available to anyone who is curious. If you genuinely want to understand the Catholic position, I'd start there.
Catechism of the Catholic Church