Considering that lady is not generally accepted as an asexual term, I'm having a difficult time parsing your statement.
Certain words mean certain things in certain contexts. If you want to start using "lady" as an asexual term, go for it. Be prepared for stares and weird looks when people don't know what you're talking about because it's not generally used that way, unlike 'dude and guy'.
The conversation was about the colloquial usage of the word dude and guy. Nothing was said about lady.