It's entirely possible that the American person who objected to the term 'lady" was a member of the radical feminist movement here in the U.S. I've been berated (I live in the western U.S.) for using the term "Ma'am" when a ddressing a member of the fair sex. That's a regional term here in the West but always known as a term of defference and respect.
The radical feminist would have every reference to differences in sex eliminated. "Person-hood" is their accepted term. To which I'm likely to respond in the same manner as I witnessed many years ago as a child.
I had the opportunity to accompany a train load of cattle, part of which had been produced by our family ranch, on it's marketing trip to Omaha, Nebraska. (at that time the reigons center of cattle marketing). I was able to achieve a ranch kids dream of going to the "big city". The ranch foreman was "Old Gus" (I never did know his real name). On arrival, we checked into the Radisson Hotel... finest place west of Chicago. It was at least ten stories tall and had an elevator.
On the ride up with Gus a most profound 'one act play' took place. On the elevator's second stop, two young women entered. Standing behind Gus, I noticed he took of his ever present Stetson hat. The women were talking as they came on, and they both became engaged in a conversation laced with profanity. Gus didn't say anything, but, almost unnoticeably (except to me) he put his hat back on. Obviously his statment that he recognized he was not in the presence of ladies. Never forgot that incident...