I agree entirely. Calling the women's team the Lady Irish is a subtle way to diminish their role and performance. It's similar to the many other ways that women are denigrated in our society. They have just as much if not more fight in them as any of the men's teams -- witness this entire season. Moreover, if it weren't for the women's teams, Notre Dame would have won many fewer championships over the past 30 years. The newspapers don't resort to that qualifier even though they may be reporting on both men's and women's teams from the same school in the same issue. Also, it sounds very Southern to me, like the Lady Vols.
I'm sure that the original poster meant no disrespect, but it hurts the women anyway.
If you insist on using Lady Irish, then it be only fair to also say Gentlemen Irish.
Finally, the University does not use that qualifier.