In the parable of the Sower (Matt. 13) I find most people think the third soil represents an unsaved person but I certainly prefer your interpretation (that he is saved), I’m just not sure about its accuracy. I stand firmly against Lordship salvation but often wonder how people can say they believe, and yet live in a way that doesn’t reflect it.
In Matt: 13:22 Jesus said the seed in the third soil represents a man who hears the word but the worries of this life and the deceitfulness of wealth choke it making it unfruitful.
A planted seed can take life and grow without bearing fruit because neither of these are fruit-bearing events. In the same way, a person can hear the word and be saved without bearing fruit because salvation is not a fruit bearing event. We bear fruit because of what we do after we’re saved. And of course, no unbeliever can ever bear fruit. Therefore the man represented by the seed in the third soil had to be a believer to even have the potential to bear fruit.
The way a believer bears fruit is to remain in a close personal relationship with the Lord, following the prompting of the Holy Spirit, and working in the strength of the Lord. According to recent polls, most believers do not do this and therefore do not bear fruit.
I am the vine, you are the branches. If a man remains in me and I in him he will bear much fruit. Apart from me you can do nothing (John 15:5).