“Incorrect. Lumen Gentium states that those without faith in Jesus Christ can be saved.”
Incorrect. Christ states in the Bible: “I am the way, the truth and the life. NO MAN comes to the Father but by me.”
A second reason why this is incorrect: If it were true, God would not have needed to command us Christians to spread the Gospel, the Good News (ie God has provided your salvation in Jesus Christ) to the rest of the world. There would be no need to if what you say is true.
The Gentiles are saved because the Word of God was taken to them and many accept it and receive Christ as Savior and Lord. They understand they can’t earn salvation any other way than Christ.
Third, Lumen Gentium is not on the same par as The Bible, which is God’s infallible Word. It is a human document and is in clear diagreement with God’s Word, therefore it is clearly wrong on the point you bring up.
I suspect the Doc is on your side of that argument.