It must be a generational thing.

I am just the opposite. Any mature female person is automatically a "lady." Especially any lady who is older than I am.
To me, that language is patronizing. Like saying there is the real football team, and then there is the Powder Puff team.
By the way, in June of this year the University of Tennessee officially changed the name of all of their women's sports teams from the "University of Tennessee Lady Volunteers" to the "University of Tennessee Volunteers Women's Team."
There was a huge outcry from alums and the public. The State Legislature jumped heatedly into the dispute. The University was forced to compromise. Now all of their women's sports team are the "Tennessee Volunteer's Women's Team," except the basketball team, who are the "Lady Vols."
(Their chief rival, the "University of Connecticut Huskies" is still affectionately known as the "Nappy-head Ho's.")