In fact, Karen didn't know how the ostentatious and luxurious villa came about. But she subconsciously felt that Lucas was a good-for-nothing who certainly wouldn't be able to afford such a villa.
It happened that she had created a misunderstanding in front of Ethan during the banquet at the Intercontinental Hotel some time ago. She had mistakenly thought that Ethan wanted Charlotte to be his daughter-in-law, only to find out later that Lucas had inadvertently done the Sawyers a huge favor. Thus, Ethan had decided to give Lucas many hefty gifts, including a luxurious sports car and properties worth several million dollars.
So Karen also took it for granted that the villa was a gift to Lucas from Ethan.
Cheyenne couldn't stand it any longer. She clarified sternly, "Mom, Lucas bought this villa, and it has nothing to do with the Sawyers."