When women’s college sports teams are added to an existing program, they often use the nickname “Lady” plus the existing men’s teams’ nickname, e.g. the “Lady Vols” of Tennessee.
What about the reverse? When men’s teams are added at a historically all-women college, do they become the “Gentlemen” something?
For example, if Sweet Briar College went co-ed, would they be the “Gentlemen Vixens”?
Here at Skidmore College, a formerly all-women’s college, is just “Thoroughbreds” for everyone.
I don’t think the use of “Lady [whatevers]” is an official usage for all women’s teams but rather a way to distinguish between sports that have both men’s and women’s teams. It’s much more common to hear “Lady [whatevers]” in basketball, where there are both men’s and women’s teams, than in softball, which is almost always a women’s team.
Personally, I find the usage a bit annoying, particularly when it’s obvious which team is being referred to.