My Protestant friend says that the Catholic Church has finally changed its teaching on justification to line up with Luther’s interpretation. True?

No, not true. Even better than true. What your friend is referring to is the Joint Declaration on the Doctrine of Justification which was signed by the Vatican and the Lutheran World Federation on October 31, 1999. See:
The document represents the culmination of decades of ecumenical dialogue at the highest levels of our two traditions on the very doctrine that was the primary dispute which many say actually caused the Reformation in the first place. It’s important to read the document to appreciate the richness of the text, but in short, it says that our two traditions have reached a common theological agreement whereby the doctrine of justification is no longer a church dividing issue. For Catholics and Lutherans to finally agree on the doctrine of justification after 500 years is something worth celebrating.