Lordship salvation theory teaches the following: That one's salvation is CONDITIONAL upon the life we live. It states:
"Submission to the will of God, to Christ’s lordship, and to the guiding of the Spirit is an essential, not an optional, part of saving faith" (EPHESIANS, p. 249).
"Salvation isn't the result of an intellectual exercise. It comes from a life lived in obedience and service to Christ as revealed in the Scripture; it's the fruit of actions, not intentions. There's no room for passive spectators: words without actions are empty and futile...The life we live, not the words we speak, determines our eternal destiny" (Hard to Believe, p. 93).
The Word of God calls it a lie in Romans 4:5... "But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness."
I suspect you are quoting MacArthur out of context.
John MacArthur is Reformed.
What he believes is that regeneration precedes faith, like all Reformed people. Therefore, God gives the person a heart of flesh to replace the heart of stone, and the fruit of this new heart is repentance and faith.
Such a person is joined to Jesus in a life-giving union. This union is productive. If the person is attached to the vine, who is Christ, he produces fruit, according to John 15 and many such sections of Scripture.
No-Lordship Salvation denies this fundamentally. Their claim is that someone can be saved, and still remain unregenerate and under the same carnal nature as before. In their worldview, regeneration makes no sense.
Christianity teaches that the person who is saved is united with Christ, and produces spiritual fruit as a result. This is what Scripture teaches.
John MacArthur is simply echoing Scripture. If guys like you misunderstand or deny Scripture, then you do so at your own risk.
James 2 says that works "justify" the person. They do not justify the person in the precise technical sense, as the sinner is justified by faith alone, but regeneration produces good fruit. The No-Lordship Salvation people deny this.
In the USA, this false teaching of No-Lordship salvation is perpetuated by disciples of Zane Hodge and Robert Wilkin, as well as many Independent Fundamentalist Baptists and the Free Grace Movement, as well as Grace Evangelical Society.
Claiming that MacArthur believes the saved person maintains his salvation through works is a lie. He is Reformed. He would believe that the saved person's union with Christ produces good works, but these good works do not maintain their salvation. The lack of good works is indicative of their lack of salvation, though. Someone who does not produce good works over their lifetime is not saved. If they continue onward in an unregenerate spirit, they don't possess salvation, or do they produce good fruit. Rotten trees don't produce good fruit.