Just from the top of my head, Melian and Galadriel. And they were not even talking about men, even though they were talking about the Noldor, but mostly it was about Galadriel herself and what she was hiding. And it is not a too long dialogue, but I think it's long enough, certainly much more than just one question and one answer, or something like that.
I am quite sure there will be something about Morwen and Nienor, like you said,
Lal, and then possibly something about Erendis and Ancalimë too... but I think the latter two will talk about men
And I think Ancalimë talks to this old woman there, her nurse or whatever should it be called, and they
definitely talk about men
But I think it's quite cool that Tolkien would pass in this test. Although I think the main point of the test is really related to the films - because I really can't think of many films which would fulfil the criteria. Even when I imagined films where many characters are women, they actually do mostly talk only about men. I am really starting to see what the person who made up the test had in mind.