Aha! Now I understand, Tom.
Yes, that’s right.
But, maybe we should go back to the “last time” stuff.
Maybe I misinterpretted what you were asking there. (Or maybe not. ;))
For these two questions, I personally would expect a time of day as the answer. In other words, these questions mean something similar to:
Q: “What time was that last appointment that you had with him?”
A: “It was at 8:30 on a Friday morning.”
That’s a very specialized sort of question. Is that what you intended?
The sentences I gave you (above) are much more general in meaning and would be answered with things such as:
“Two months ago”
That’s why I said that they sounded more natural to me. They are more commonly used/needed. And they ask the question I thought you wanted to ask.